Broadband digital beam forming system including wavefront multiplexers and narrowband digital beam forming modules

ABSTRACT

A broadband digital beam forming system comprises a set of Q pre-processing modules, Q being an integer greater than or equal to 2, and a set of M digital beam forming modules in communication with the Q preprocessing modules. Each of the Q preprocessing modules receives a respective one of Q broadband input signal streams and outputs M narrowband signal streams, M being an integer greater than or equal to 2. The total number of narrowband signal streams outputted by the Q pre-processing modules is Q times M. Each of the M digital beam forming modules receives corresponding Q narrowband signal streams of the Q times M narrowband signal streams, and outputs R beam signals, R being an integer greater than or equal to 1. The system further comprises a set of R post-processing modules in communication with the M digital beam forming modules. Each of the R post-processing modules receives M beam signals, each of the M beam signals being a corresponding one of the R beam signals from each of the M digital beam forming modules, and outputs a corresponding broadband output signal.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of application Ser. No. 14/580,248 filed on Dec. 23, 2014, which is a continuation of application Ser. No. 13/525,315, filed on Jun. 17, 2012, issued as U.S. Pat. No. 8,953,728, which claims the benefit of U.S. Provisional Application Ser. No. 61/497,852, filed on Jun. 16, 2011, all of which are herein incorporated by reference in their entirety.

BACKGROUND OF THE DISCLOSURE

Field of the Disclosure

The disclosure relates to a signal or data stream processing system, and more particularly, to a signal or data stream processing system that includes a wave-front multiplexer and a wave-front demultiplexer that is complementary transformation to the wave-front multiplexer.

Brief Description of the Related Art

Signal processing is a mathematical manipulation of a signal to transform, modify or improve it in some way. For example, signals can be constantly converted from analog to digital, manipulated digitally, and then converted back to analog form. Signal processing algorithms requires a large number of mathematical operations to be performed quickly and repeatedly on a signal.

SUMMARY OF THE DISCLOSURE

The present invention provides exemplary approaches of coherent combining parallel processing that are proposed addressing various application enhancements. Proposed algorithms may include pre-processing of signals in a multi-channel structure for diagnostics of multiple unequalized propagation/processing delay paths at the input end, and associated adaptive post processing at an output end. The preprocessors generate orthogonality among various wavefronts and attach various inputs to different wavefronts. The post processing iteratively equalizes phases/amplitudes and/or time delays among the multiple paths via different processors, or propagation sub-channels based only on the diagnostic information gained by unique structure Rx signals. As a result of successful compensations, the orthogonality among wavefronts are restored. Therefore the individual outputs associated with various inputs can then be reconstituted. The organized structure for the multiple processing subchannels is the wave-front multiplexing/de-multiplexing (WF Muxing/De-muxing) processing. There requires no feedback paths between transmit (Tx) and receiving (Rx) ends. Therefore, no back channel exchange is required for the calibrations and equalizations among various processing or propagation paths, or sub-channels, and thus minimizing potential complexity in control algorithms.

There may be needs for fragmenting high bandwidth signals into multiple sub-channels due to shortage of continuous spectrum or speed of available processors. It is desirable to decompose a wideband signal stream, from a transmit end, into multiple subband signals, and then having them frequency converted individually to various sub-channels at different frequency slots before transmission. At Rx end of the link, captured sub-channel signals are frequency converted back to those of individual subbands. The wideband signal stream is then reconstituted through proper processing on these Rx subband signals.

There may be also needs for fragmenting high bandwidth signals into multiple sub-channels due to processing speed of available processors. It is desirable to decompose a wideband signal stream, from an input, into multiple subband signals, and then having them processed by different processors at lower speed concurrently. At output end of the processing, captured sub-channel signals are re-constituted back to the wideband signal stream through proper processing on these Rx subband signals.

There may be also needs for combining multiple devices in parallel to gain better performance in power outputs, enhanced dynamic range, higher proceeding bandwidth/speed, better transmissions or processing securities, and/or combinations of above.

An exemplary embodiment of the present disclosure provides a system for processing data streams or signals including a wave-front multiplexer configured to process first and second input signals into first and second output signals each carrying information associated with the first and second input signals, a first processing unit or device configured to process a third input signal carrying information associated with the first output signal into a third output signal, a second processing unit or device configured to process a fourth input signal carrying information associated with the second output signal into a fourth output signal, and a wave-front demultiplexer configured to process fifth and sixth input signals into fifth and sixth output signals each carrying information associated with the fifth and sixth input signals. The fifth input signal carries information associated with the third output signal, and the sixth input signal carries information associated with the fourth output signal.

Another exemplary embodiment of the present disclosure provides a system for transmitting data streams or signals including a wave-front multiplexer configured to process first and second input signals into first and second output signals each carrying information associated with the first and second input signals, a communication medium configured to transmit a first transmitting signal carrying information associated with the first output signal and transmit a second transmitting signal carrying information associated with the second output signal, and a wave-front demultiplexer configured to process third and fourth input signals into third and fourth output signals each carrying information associated with the third and fourth input signals. The third input signal carries information associated with the first transmitting signal, and the fourth input signal carries information associated with the second transmitting signal. The third output signal is substantially equal to the first input signal, and the fourth output signal is substantially equal to the second input signal. Alternative, the third output signal is equal to the first input signal multiplied by a first scalar, and the fourth output signal is equal to the second input signal by a second scalar, wherein the first scalar is substantially equal to the second scalar.

These, as well as other components, steps, features, benefits, and advantages of the present disclosure, will now become clear from a review of the following detailed description of illustrative embodiments, the accompanying drawings, and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings disclose illustrative embodiments of the present disclosure. They do not set forth all embodiments. Other embodiments may be used in addition or instead. Details that may be apparent or unnecessary may be omitted to save space or for more effective illustration. Conversely, some embodiments may be practiced without all of the details that are disclosed. When the same reference number or reference indicator appears in different drawings, it may refer to the same or like components or steps.

Aspects of the disclosure may be more fully understood from the following description when read together with the accompanying drawings, which are to be regarded as illustrative in nature, and not as limiting. The drawings are not necessarily to scale, emphasis instead being placed on the principles of the disclosure. In the drawings:

FIG. 1A shows a system including a wave-front multiplexer, a wave-front demultiplexer and multiple signal processing units or devices according to an embodiment of the present disclosure;

FIG. 1B shows a system including a wave-front multiplexer, a wave-front demultiplexer, multiple signal processing units or devices, an equalizer, and an optimizer according to an embodiment of the present disclosure;

FIG. 1C shows a flow chart of an optimizing and equalizing process according to an embodiment of the present disclosure;

FIG. 1D shows architecture of a wave-front multiplexer according to an embodiment of the present disclosure;

FIG. 1E shows architecture of a wave-front demultiplexer according to an embodiment of the present disclosure;

FIG. 2A shows an A/D conversion system including a wave-front multiplexer, four A/D converters and a wave-front demultiplexer according to an embodiment of the present disclosure;

FIG. 2B shows an A/D conversion system including a wave-front multiplexer, four A/D converters, a wave-front demultiplexer, an equalizer and an optimizer according to an embodiment of the present disclosure;

FIG. 2C shows an A/D conversion system including a wave-front multiplexer, eight frequency down-conversion components, eight A/D converters, a wave-front demultiplexer, an equalizer and an optimizer according to an embodiment of the present disclosure;

FIG. 2D shows an A/D conversion system including a wave-front multiplexer, four frequency down-conversion components, four A/D converters, a wave-front demultiplexer, an equalizer, an optimizer and a 4-to-1 time-division multiplexer according to an embodiment of the present disclosure;

FIG. 3A shows a broadband DBFN system including sixteen preprocessor modules, four narrowband DBFN modules and four post-processor modules according to an embodiment of the present disclosure;

FIG. 3B shows a scheme of a narrowband DBFN module according to an embodiment of the present disclosure;

FIG. 3C shows a broadband DBFN system including sixteen preprocessor modules, eight narrowband DBFN modules and four post-processor modules according to an embodiment of the present disclosure;

FIG. 3D shows a broadband DBFN system including thirty-two preprocessor modules, sixteen narrowband DBFN modules and four post-processor modules according to an embodiment of the present disclosure;

FIG. 3E shows architecture of a preprocessor module according to an embodiment of the present disclosure;

FIG. 3F shows architecture of a post-processor module according to an embodiment of the present disclosure;

FIG. 3G shows architecture of a narrowband DBFN module according to an embodiment of the present disclosure;

FIG. 4A shows a broad-band linear processing system including a 1-to-3 time-domain demultiplexer, a wave-front multiplexer, four narrowband linear processors, a wave-front demultiplexer, an equalizer, an optimizer and a 3-to-1 time-domain multiplexer according to an embodiment of the present disclosure;

FIG. 4B shows a broad-band linear processing system including a 1-to-M time-domain demultiplexer, a wave-front multiplexer, multiple narrowband linear processors, a wave-front demultiplexer, an equalizer, an optimizer and a M-to-1 time-domain multiplexer according to an embodiment of the present disclosure;

FIG. 4C shows a broad-band linear processing system including a preprocessor module, sixteen narrowband linear processors, and a post-processor module according to an embodiment of the present disclosure;

FIG. 4D shows a broad-band linear processing system including a preprocessor module, sixteen narrowband linear processors, and a post-processor module according to an embodiment of the present disclosure;

FIG. 4E shows a broad-band linear processing system including a wave-front multiplexer, four narrowband linear processors, a wave-front demultiplexer, an equalizer and an optimizer according to an embodiment of the present disclosure;

FIG. 4F shows a calculation of a broad-band linear processing system according to an embodiment of the present disclosure;

FIG. 5A shows a system including a wave-front multiplexer, four optical transmit devices, four optical detectors, a MGDM device, a MGDDM device, a multimode fiber, a wave-front demultiplexer, an equalizer and an optimizer according to an embodiment of the present disclosure;

FIG. 5B shows a mathematical model of mode-coupling among four propagation paths in a multimode fiber according to an embodiment of the present disclosure;

FIG. 5C shows a system including a 1-to-3 time-domain demultiplexer, a wave-front multiplexer, four optical transmit devices, four optical detectors, a MGDM device, a MGDDM device, a multimode fiber, a wave-front demultiplexer, an equalizer, an optimizer and a 3-to-1 time-domain multiplexer according to an embodiment of the present disclosure;

FIG. 5D shows a system including a 1-to-3 time-domain demultiplexer, two wave-front multiplexers, two sets of four optical transmit devices, a set of four optical detectors, two MGDM devices, a MGDDM device, a multimode fiber, a wave-front demultiplexer, an equalizer, an optimizer and a 3-to-1 time-domain multiplexer according to an embodiment of the present disclosure;

FIG. 5E shows a system including a 1-to-250 time-domain demultiplexer, a wave-front multiplexer, eight 32-to-1 time-domain multiplexers, eight optical transmit devices, eight optical detectors, a MGDM device, a MGDDM device, a multimode fiber, eight 1-to-32 time-domain demultiplexers, a wave-front demultiplexer, an equalizer, an optimizer and a 250-to-1 time-domain multiplexer according to an embodiment of the present disclosure;

FIG. 5F shows a system including a 1-to-50 time-domain demultiplexer, a 1-to-170 time-domain demultiplexer, a 1-to-30 time-domain demultiplexer, a wave-front multiplexer, eight 32-to-1 time-domain multiplexers, eight optical transmit devices, eight optical detectors, a MGDM device, a MGDDM device, a multimode fiber, eight 1-to-32 time-domain demultiplexers, a wave-front demultiplexer, an equalizer, an optimizer, a 50-to-1 time-domain multiplexer, a 170-to-1 time-domain multiplexer and a 30-to-1 time-domain multiplexer according to an embodiment of the present disclosure;

FIGS. 5G and 5H show a system including a 1-to-50 time-domain demultiplexer, a 1-to-170 time-domain demultiplexer, a 1-to-30 time-domain demultiplexer, two wave-front multiplexers, two sets of eight 32-to-1 time-domain multiplexers, two sets of eight optical transmit devices, two MGDM devices, a multimode fiber, a MGDDM device, a set of eight optical detectors, a set of eight 1-to-32 time-domain demultiplexers, an equalizer, a wave-front demultiplexer, an optimizer, a 50-to-1 time-domain multiplexer, a 170-to-1 time-domain multiplexer and a 30-to-1 time-domain multiplexer according to an embodiment of the present disclosure;

FIG. 6A shows a system including an uplink ground terminal, two antenna arrays, a satellite and a downlink ground terminal according to an embodiment of the present disclosure;

FIG. 6B shows a system including an uplink ground terminal, two antenna arrays, two satellites and a downlink ground terminal according to an embodiment of the present disclosure;

FIGS. 6C and 6D show a system including two uplink ground terminals, three antenna arrays, two satellites and a downlink ground terminal according to an embodiment of the present disclosure;

FIG. 7A shows a power amplifying system including a wave-front multiplexer, four power amplifiers and a wave-front demultiplexer according to an embodiment of the present disclosure;

FIG. 7B shows a power amplifying system including a wave-front multiplexer, an equalizer, four power amplifiers and a wave-front demultiplexer according to an embodiment of the present disclosure;

FIG. 7C shows a power amplifying system including a wave-front multiplexer, an equalizer, four power amplifiers, a wave-front demultiplexer and an optimizer according to an embodiment of the present disclosure;

FIG. 7D shows a power amplifying system including a wave-front multiplexer, an equalizer, four frequency up-conversion components, four power amplifiers, a wave-front demultiplexer and an optimizer according to an embodiment of the present disclosure; and

FIG. 7E shows a power amplifying system including a wave-front multiplexer, an equalizer, eight frequency up-conversion components, eight power amplifiers, a wave-front demultiplexer and an optimizer according to an embodiment of the present disclosure.

While certain embodiments are depicted in the drawings, one skilled in the art will appreciate that the embodiments depicted are illustrative and that variations of those shown, as well as other embodiments described herein, may be envisioned and practiced within the scope of the present disclosure.

DETAILED DESCRIPTION OF THE INVENTION

Illustrative embodiments are now described. Other embodiments may be used in addition or instead. Details that may be apparent or unnecessary may be omitted to save space or for a more effective presentation. Conversely, some embodiments may be practiced without all of the details that are disclosed.

Before describing embodiments of the present invention, a definition has been included for these various terms. These definitions are provided to assist in teaching a general understanding of the present invention.

Wave-Front Multiplexer (WF Muxer):

The term “wave-front multiplexer” is used herein to denote a specialized signal processing transform from a spatial-domain representation of signals to a wavefront-domain representation of the signals. A wave-front multiplexer performs an orthogonal functional transformation to multiply an orthogonal matrix, such as Fourier matrix, Butler matrix or Hadamard matrix, by an input matrix representing multiple input signals so as to obtain an output matrix representing multiple output signals. The orthogonal functional transformation can be, but not limited to, Fourier transformation, discrete Fourier transformation (DFT), fast Fourier transformation (FFT), Hartley transformation, Hadamard transformation, or any other Fourier-related transformation. Each output signal output from the wave-front multiplexer is a linear combination, i.e. weighted sum, of all input signals input into the wave-front multiplexer. As a result, each input signal into the wave-front multiplexer appears in all output signals. The weightings of one input signal among all the output signals feature a unique distribution which is defined as a wavefront multiplexing vector (WFMV). When the wave-front multiplexer features H inputs receiving H input signals and H outputs outputting H output signals, there are H wavefront multiplexing vectors (WFMVs) associated with the H inputs of the H-to-H wave-front multiplexer, and each of the H wavefront multiplexing vectors is an H-dimensional vector, where H is an integer equal to or greater than two, four, eight, sixteen, thirty-two, sixty-four or two-hundred-and-fifty-six. The H wavefront multiplexing vectors are mutually orthogonal to one another. Each of the H output signals carries a linear combination of all the H input signals, and the H input signals appearing in each of the H output signals can be completely independent from one another. The above-mentioned transform performed by the wave-front multiplexer is called herein a wave-front multiplexing transform or transformation, which can be applied to the following embodiments.

The wave-front multiplexing transform may be, but not limited to, implemented at base band in a digital format or by analog devices, wherein the devices may be selected from a group consisting of a Butler Matrix, a Fourier transform, and a Hartley transform.

The wave-front multiplexer can be, but not limited to, embedded in a processor. The wave-front multiplexer can be implemented by hardware which performing the above wave-front multiplexing transformation, such as FFT chip, Butler matrix, or a device performing a specified transformation of an orthogonal matrix such as Fourier matrix or Hadamard matrix. Alternatively, the function of the wave-front multiplexer can be realized by software installed in and performed by the processor, wherein the software can perform the above wave-front multiplexing transform. Alternatively, the wave-front multiplexer can be or include, but not limited to, a field programmable gate array (FPGA) or a digital signal processor (DSP).

The wave-front multiplexer can be layout with circuits for cells of basic functions recorded in a cell library such that any company of interest can implement the circuit layout in an integrated-circuit chip, a system-on chip (SOC) or an integrated-circuit chip package.

The wave-front multiplexer (WF muxer) features multiple-input and multiple-output (MIMO) processing that receives multiple input signals passing in parallel through multiple parallel input ports of the WF muxer and outputs multiple output signals passing in parallel through multiple parallel output ports of the WF muxer. The total number of the parallel input ports of the WF muxer may be equal to the total number of the parallel output ports of the WF muxer, may be equal to the number of rows or columns of an orthogonal matrix characterizing the WF muxer, and may be any number equal to or more than two, four, eight, sixteen, thirty-two or two-hundred-and-fifty-six. The total number of the input signals into the WF muxer may be equal to or less than the total number of the parallel input ports of the WF muxer, may be equal to or less than the number of rows or columns of the orthogonal matrix characterizing the WF muxer, and may be any number equal to or more than two, four, eight, sixteen, thirty-two or two-hundred-and-fifty-six. The total number of the output signals output form the WF muxer may be equal to the total number of the parallel output ports of the WF muxer, may be equal to the number of rows or columns of the orthogonal matrix characterizing the WF muxer, and may be any number equal to or more than two, four, eight, sixteen, thirty-two or two-hundred-and-fifty-six.

Wave-Front Demultiplexer (WF Demuxer):

The term “Wave-front demultiplexer” is used herein to denote a specialized signal processing transform from a wavefront-domain representation of signals to a spatial-domain representation of the signals. A wave-front demultiplexer performs a complementary transformation to a wave-front multiplexer and extracts multiple signals each corresponding to one of the original signals input to the wave-front multiplexer.

The wave-front demultiplexer performs an inverse orthogonal functional transformation to multiply an inverse orthogonal matrix, such as inverse Fourier matrix, Butler matrix or Hadamard matrix, by an input matrix representing multiple input signals so as to obtain an output matrix representing multiple output signals. The inverse transformation performed by the wave-front demultiplexer is the inverse of the transformation performed by a corresponding or complementary wave-front multiplexer. Many orthogonal matrixes, such as Hadamard matrix, have inverses which equal to the orthogonal matrixes themselves. The inverse orthogonal functional transformation can be, but not limited to, inverse Fourier transformation, inverse discrete Fourier transformation, inverse fast Fourier transformation (IFFT), Hadamard transformation, inverse Hartley transformation, any other inverse Fourier-related transformation, or any transformation of an orthogonal matrix (such as inverse Fourier matrix, Butler matrix, or Hadamard matrix).

Hadamard transforms featuring the inverse transforms equal to themselves may be used for the wave-front multiplexing and demultiplexing transforms. In the present disclosure, the wave-front multiplexing and demultiplexing transforms can be, but not limited to, characterized by same matrixes.

Alternatively, the wave-front multiplexing transform may have an inverse not equal to itself. The wave-front multiplexing transform is not equal to the corresponding or complementary wave-front demultiplexing transform. For example, the wave-front multiplexing and demultiplexing transforms can be, but not limited to, a fast Fourier transform (FFT) and its corresponding or complementary inverse fast Fourier transforms (IFFT).

Each output signal output from the wave-front demultiplexer is a linear combination, i.e. weighted sum, of all input signals input into the wave-front demultiplexer. As a result, each input signal into the wave-front demultiplexer appears in all output signals. The weightings of one input signal among all the output signals feature a unique distribution which is defined as a wavefront demultiplexing vector (WFDV). When the wave-front demultiplexer features I inputs receiving I input signals and I outputs outputting I output signals, there are I wavefront demultiplexing vectors (WFDVs) associated with the I inputs of the I-to-I wave-front demultiplexer, and each of the I wavefront demultiplexing vectors is an I-dimensional vector, where I is an integer equal to or greater than two, four, eight, sixteen, thirty-two, sixty-four or two-hundred-and-fifty-six. The I wavefront demultiplexing vectors are mutually orthogonal to one another. Each of the I output signals carries a linear combination of all the I input signals, and the I input signals appearing in each of the I output signals can be completely independent from one another.

Therefore, the wave-front demultiplexer extracts coherently combined signals from input signals input to the wave-front demultiplexer and outputs the coherently combined signals, such that each of the coherently combined signals output from the wave-front demultiplexer can be correspondent to or associated with one of the input signals input into the wave-front multiplexer. The above-mentioned transform performed by the wave-front demultiplexer is called herein a wave-front demultiplexing transform or transformation, which can be applied to the following embodiments.

The wave-front demultiplexer can be, but not limited to, embedded in a processor. The wave-front demultiplexer can be implemented by hardware which performing the above wave-front demultiplexing transformation, such as IFFT chip, Butler matrix, or a device performing a specified transformation of an inverse orthogonal matrix. Alternatively, the function of the wave-front demultiplexer can be realized by software installed in and performed by the processor, wherein the software can perform the above wave-front demultiplexing transform. Alternatively, the wave-front demultiplexer can be or include, but not limited to, a field programmable gate array (FPGA) or a digital signal processor (DSP). When the wave-front multiplexing and demultiplexing transformations are implemented by hardware, the wave-front multiplexer and the wave-front demultiplexer can be, but not limited to, a pair of Butler Matrixes, a Fourier transform pair, or a Hartley transform pair.

The wave-front demultiplexer can be layout with circuits for cells of basic functions recorded in a cell library such that any company of interest can implement the circuit layout in an integrated-circuit chip, a system-on chip (SOC) or an integrated-circuit chip package.

The wave-front demultiplexer (WF demuxer) features multiple-input and multiple-output (MIMO) processing that receives multiple input signals passing in parallel through multiple parallel input ports of the WF demuxer and outputs multiple output signals passing in parallel through multiple parallel output ports of the WF demuxer. The total number of the parallel input ports of the WF demuxer may be equal to the total number of the parallel output ports of the WF demuxer, may be equal to the total number of parallel input ports of a corresponding or complementary WF muxer, may be equal to the total number of parallel output ports of the corresponding or complementary WF muxer, may be equal to the number of rows or columns of an orthogonal matrix characterizing the corresponding or complementary WF muxer, may be equal to the number of rows or columns of an inverse orthogonal matrix characterizing the WF demuxer, and may be any number equal to or more than two, four, eight, sixteen, thirty-two or two-hundred-and-fifty-six. The total number of the input signals input in parallel to the WF demuxer may be equal to the total number of output signals output in parallel from the corresponding or complementary WF muxer, may be equal to the total number of the parallel inputs of the WF demuxer, and may be any number equal to or more than two, four, eight, sixteen, thirty-two or two-hundred-and-fifty-six. The total number of the output signals output in parallel form the WF demuxer may be equal to the total number of input signals input in parallel to the corresponding or complementary WF muxer, may be equal to or less than the total number of the input signals input in parallel to the WF demuxer, may be equal to or less than the total number of the output signals output in parallel from the corresponding or complementary WF muxer, may be equal to or less than the total number of the parallel output ports of the WF demuxer, and may be any number equal to or more than two, four, eight, sixteen, thirty-two or two-hundred-and-fifty-six.

Mathematically, the wave-front demultiplexing transformation can be expressed by a linear equation as Z=WFDM*S, where S denotes input vectors such as four components S₁-S₄ in the following matrix D as illustrated in FIG. 1A, Z denotes output vectors such as four components in the following matrix F as illustrated in FIG. 1A, and WFDM denotes an inverse orthogonal matrix, such as the following matrix E as illustrated in FIG. 1A, of the wave-front demultiplexer. The wave-front multiplexing transformation can be expressed by a linear equation as Y=WFM*X, where X denotes input vectors such as four components X₁-X₄ in the following matrix A as illustrated in FIG. 1A, Y denotes output vectors such as four components in the following matrix C as illustrated in FIG. 1A, and WFM denotes an orthogonal matrix, such as the following matrix B as illustrated in FIG. 1A, of the wave-front multiplexer. The wave-front demultiplexing transformation features the characteristic that WFM*WFDM=I, where I is a unit matrix. Basically, WFM and WFDM are square matrices, and the order of WFM has the same rows and columns as the order of WFDM. For example, in case the orders of WFM and WFDM each having N rows and N columns are N×N, each of the wave-front multiplexing and demultiplexing transformations is available to processing N input vectors, i.e. input signals, and transforming the N input vectors into N output vectors, i.e. output signals, where N is an integer equal to or greater than two, four, eight, sixteen, thirty-two or two-hundred-and-fifty-six.

The wave-front demultiplexer, for example, can be used at a receiving side of a system with a complementary wave-front multiplexer at a transmitting side of the system, and multiple signal paths, such as physical or wireless channels, can be set between an antenna array of the transmitting side and an antenna array of the receiving side. Satellite transponders can be arranged in the signal paths between the antenna array of the transmitting side and the antenna array of the receiving side. Alternatively, both of the wave-front demultiplexer and complementary wave-front multiplexer can be arranged at the receiving side of the system. Alternatively, both of the wave-front demultiplexer and complementary wave-front multiplexer can be arranged at the transmitting side of the system.

The above-mentioned descriptions of the wave-front multiplexer and the wave-front demultiplexer can be applied to the following embodiments.

FIG. 1A shows an example illustrating how a four-input and four-output wave-front multiplexer along with a four-input and four-output wave-front demultiplexer works.

Referring to FIG. 1A, a system 888 includes a wave-front multiplexer 213, a wave-front demultiplexer 232, and multiple signal processing units or devices such as four units or devices 999 a, 999 b, 999 c and 999 d. Each of the wave-front multiplexer 213 and the wave-front multiplexer 232 can be, but not limited to, a four-input and four-output unit. That is, the wave-front multiplexer 213 may have four inputs 2 a, 2 b, 2 c and 2 d and four outputs 3 a, 3 b, 3 c and 3 d, and the wave-front demultiplexer 232 may have four inputs 6 a, 6 b, 6 c and 6 d and four outputs 7 a, 7 b, 7 c and 7 d.

The signal processing units or devices 999 a, 999 b, 999 c and 999 d, for example, can be embedded in a processor 998 or can be respectively embedded in four processors such as four mobile or wireless communication base stations, four satellites, four mobile phones, four computers, or four servers. The processor 998 can be, but not limited to, a mobile or wireless communication base station, a satellite, a mobile phone, a computer, or a server. The signal processing unit or device 999 a is in a first signal path between the output 3 a of the wave-front multiplexer 213 and the input 6 a of the wave-front demultiplexer 232, being used to process an input signal, such as signal Y₁ output from the output 3 a, so as to output another signal, such as signal S₁. The signal processing unit or device 999 b is in a second signal path between the output 3 b of the wave-front multiplexer 213 and the input 6 b of the wave-front demultiplexer 232, being used to process an input signal, such as signal Y₂ output from the output 3 b, so as to output another signal, such as signal S₂. The signal processing unit or device 999 c is in a third signal path between the output 3 c of the wave-front multiplexer 213 and the input 6 c of the wave-front demultiplexer 232, being used to process an input signal, such as signal Y₃ output from the output 3 c, so as to output another signal, such as signal S₃. The signal processing unit or device 999 d is in a fourth signal path between the output 3 d of the wave-front multiplexer 213 and the input 6 d of the wave-front demultiplexer 232, being used to process an input signal, such as signal Y₄ output from the output 3 d, so as to output another signal, such as signal S₄. The first, second, third and fourth signal paths are arranged in parallel.

There are four input signals X₁, X₂, X₃ and X₄ input in parallel to the four inputs 2 a, 2 b, 2 c and 2 d of the wave-front multiplexer 213. The signals X₁, X₂, X₃ and X₄ can be, but not limited to, digital signals, analog signals, mixed analog and digital signals, or digital signal streams. Next, the wave-front multiplexer 213 performs the wave-front multiplexing transform to multiply the four input signals X₁, X₂, X₃ and X₄, represented by a 4×1 input matrix A, by an orthogonal matrix B so as to obtain four output signals Y₁, Y₂, Y₃ and Y₄ represented by a 4×1 output matrix C and then outputs the four output signals Y₁, Y₂, Y₃ and Y₄ from its four outputs 3 a, 3 b, 3 c and 3 d. The matrix B is a square matrix, and the transpose of the matrix B is equal to the inverse of the matrix B. The below formula (1) illustrates the input matrix A multiplied by the orthogonal matrix B, performed on the wave-front multiplexer 213.

$\begin{matrix} {{{{matrix}\mspace{14mu} A} = \begin{bmatrix} X_{1} \\ X_{2} \\ X_{3} \\ X_{4} \end{bmatrix}}{{{matrix}\mspace{14mu} B} = \begin{bmatrix} C_{11} & C_{12} & C_{13} & C_{14} \\ C_{21} & C_{22} & C_{23} & C_{24} \\ C_{31} & C_{32} & C_{33} & C_{34} \\ C_{41} & C_{42} & C_{43} & C_{44} \end{bmatrix}}{{{matrix}\mspace{14mu} C} = {{\begin{bmatrix} {{C_{11}X_{1}} + {C_{12}X_{2}} + {C_{13}X_{3}} + {C_{14}X_{4}}} \\ {{C_{21}X_{1}} + {C_{22}X_{2}} + {C_{23}X_{3}} + {C_{24}X_{4}}} \\ {{C_{31}X_{1}} + {C_{32}X_{2}} + {C_{33}X_{3}} + {C_{34}X_{4}}} \\ {{C_{41}X_{1}} + {C_{42}X_{2}} + {C_{43}X_{3}} + {C_{44}X_{4}}} \end{bmatrix}\begin{bmatrix} C_{11} & C_{12} & C_{13} & C_{14} \\ C_{21} & C_{22} & C_{23} & C_{24} \\ C_{31} & C_{32} & C_{33} & C_{34} \\ C_{41} & C_{42} & C_{43} & C_{44} \end{bmatrix}}{\quad{\begin{bmatrix} X_{1} \\ X_{2} \\ X_{3} \\ X_{4} \end{bmatrix} = {\begin{bmatrix} {{C_{11}X_{1}} + {C_{12}X_{2}} + {C_{13}X_{3}} + {C_{14}X_{4}}} \\ {{C_{21}X_{1}} + {C_{22}X_{2}} + {C_{23}X_{3}} + {C_{24}X_{4}}} \\ {{C_{31}X_{1}} + {C_{32}X_{2}} + {C_{33}X_{3}} + {C_{34}X_{4}}} \\ {{C_{41}X_{1}} + {C_{42}X_{2}} + {C_{43}X_{3}} + {C_{44}X_{4}}} \end{bmatrix} = \begin{bmatrix} Y_{1} \\ Y_{2} \\ Y_{3} \\ Y_{4} \end{bmatrix}}}}}}} & (1) \end{matrix}$

The components associated with the input X₁ in the four outputs are in the forms of C₁₁X₁, C₂₁X₁, C₃₁X₁ and C₄₁X₁. The weighting distribution of the components associated with the input X₁ in the four outputs is characterized by a first column vector, i.e. first wave-front multiplexing vector (WFMV1), where

${{WFMV}\; 1} = \begin{bmatrix} C_{11} \\ C_{21} \\ C_{31} \\ C_{41} \end{bmatrix}$

Similarly, the components associated with the input X₂ in the four outputs are in the forms of C₁₂X₂, C₂₂X₂, C₃₂X₂ and C₄₂X₂. The weighting distribution of the components associated with the input X₂ in the four outputs is characterized by a second column vector, i.e. second wave-front multiplexing vector (WFMV2), where

${{WFMV}\; 2} = \begin{bmatrix} C_{12} \\ C_{22} \\ C_{32} \\ C_{42} \end{bmatrix}$

The components associated with the input X₃ in the four outputs are in the forms of C₁₃X₃, C₂₃X₃, C₃₃X₃ and C₄₃X₃. The weighting distribution of the components associated with the input X₃ in the four outputs is characterized by a third column vector, i.e. third wave-front multiplexing vector (WFMV3), where

${{WFMV}\; 3} = \begin{bmatrix} C_{13} \\ C_{23} \\ C_{33} \\ C_{43} \end{bmatrix}$

The components associated with the input X₄ in the four outputs are in the forms of C₁₄X₄, C₂₄X₄, C₃₄X₄ and C₄₄X₄. The weighting distribution of the components associated with the input X₄ in the four outputs is characterized by a fourth column vector, i.e. fourth wave-front multiplexing vector (WFMV4), where

${{WFMV}\; 4} = \begin{bmatrix} C_{14} \\ C_{24} \\ C_{34} \\ C_{44} \end{bmatrix}$

The first and second wave-front multiplexing vectors are mutually orthogonal to each other. The first and third wave-front multiplexing vectors are mutually orthogonal to each other. The first and fourth wave-front multiplexing vectors are mutually orthogonal to each other. The second and third wave-front multiplexing vectors are mutually orthogonal to each other. The second and fourth wave-front multiplexing vectors are mutually orthogonal to each other. The third and fourth multiplexing wave-front vectors are mutually orthogonal to each other.

The output signal Y₁ is a linear combination, i.e. weighted sum, of all input signals X₁, X₂, X₃ and X₄ multiplied by the weightings C₁₁, C₁₂, C₁₃, and C₁₄, respectively. That is, the output signal Y₁ can be represented by a linear combination of C₁X₁ plus C₁₂X₂ plus C₁₃X₃ plus C₁₄X₄. The four input signals X₁, X₂, X₃ and X₄ can be completely independent. The output signal Y₂ is a linear combination, i.e. weighted sum, of all input signals X₁, X₂, X₃ and X₄ multiplied by the weightings C₂₁, C₂₂, C₂₃, and C₂₄, respectively. That is, the output signal Y₂ can be represented by a linear combination of C₂₁X₁ plus C₂₂X₂ plus C₂₃X₃ plus C₂₄X₄. The output signal Y₃ is a linear combination, i.e. weighted sum, of all input signals X₁, X₂, X₃ and X₄ multiplied by the weightings C₃₁, C₃₂, C₃₃, and C₃₄, respectively. That is, the output signal Y₃ can be represented by a linear combination of C₃₁X₁ plus C₃₂X₂ plus C₃₃X₃ plus C₃₄X₄. The output signal Y₄ is a linear combination, i.e. weighted sum, of all input signals X₁, X₂, X₃ and X₄ multiplied by the weightings C₄₁, C₄₂, C₄₃, and C₄₄, respectively. That is, the output signal Y₄ can be represented by a linear combination of C₁X₁ plus C₄₂X₂ plus C₄₃X₃ plus C₄₄X₄.

Therefore, each of the output signals Y₁, Y₂, Y₃ and Y₄ output from the wave-front multiplexer 213 is a linear combination, i.e. weighted sum, of all input signals X₁, X₂, X₃ and X₄ multiplied by respective weightings, and distributions of the weightings of any two input components in the four output signals Y₁, Y₂, Y₃ and Y₄ are orthogonal. The weightings include C₁₁, C₁₂, C₁₃ and C₁₄ for the input signals X₁, X₂, X₃ and X₄, respectively, in the output signal Y₁, include C₂₁, C₂₂, C₂₃ and C₂₄ for the input signals X₁, X₂, X₃ and X₄, respectively, in the output signal Y₂, include C₃₁, C₃₂, C₃₃ and C₃₄ for the input signals X₁, X₂, X₃ and X₄, respectively, in the output signal Y₃, and include C₄₁, C₄₂, C₄₃ and C₄₄ for the input signals X₁, X₂, X₃ and X₄, respectively, in the output signal Y₄.

In other words, each of the output signals Y₁, Y₂, Y₃ and Y₄ is processed by multiple factors including the input signals X₁, X₂, X₃ and X₄ and the corresponding weightings. For the output signal Y₁, the factors include the input signals X₁, X₂, X₃ and X₄ and their weightings C₁₁, C₁₂, C₁₃ and C₁₄. For the output signal Y₂, the factors include the input signals X₁, X₂, X₃ and X₄ and their weightings C₂₁, C₂₂, C₂₃ and C₂₄. For the output signal Y₃, the factors include the input signals X₁, X₂, X₃ and X₄ and their weightings C₃₁, C₃₂, C₃₃ and C₃₄. For the output signal Y₄, the factors include the input signals X₁, X₂, X₃ and X₄ and their weightings C₄₁, C₄₂, C₄₃ and C₄₄.

Referring to FIG. 1D showing architecture of a wave-front multiplexer in accordance with the present invention. For more elaboration, the wave-front multiplexer can be adapted to receive the number H of input signals X, process the number H of the input signals X to be multiplied by the above-mentioned WFM matrix, such as H-by-H square orthogonal matrix, and output the number H of output signals Y, wherein H could be any number greater than or equal to 2, 4, 8, 16, 32, 64, 126 or 256. The input signals X can be, but not limited to, analog or digital signals. The output signals Y can be, but not limited to, analog or digital signals. The wave-front multiplexer may include the number H*H of computing units (CUs) and the number H of summing processors (SPs). The computing units form an H-by-H processor array with the number H of columns and the number H of rows. The computing units in each column in the processor array receive a corresponding input signal X, and thus the number H of the input signals X can be received by the computing units in the number H of the respective columns in the processor array. Upon receiving the input signals X, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. Each of the summing processors provides a means for summing weighted signals generated by the corresponding computing units in same row in the processor array to produce a corresponding output signal Y. Accordingly, the number H of the summing processors can output the number H of the output signals Y each combined with the weighted signals output from the computing units in a corresponding one of the number H of the rows in the processor array. The above-mentioned description of the wave-front multiplexer can be applied to the following embodiments.

In the case illustrated in FIG. 1A, the number of H is equal to 4. The wave-front multiplexer 213 illustrated in FIG. 1A may include 4*4 computing units and four summing processors. The computing units form a processor array with four rows and four columns. The input signals X₁-X₄ illustrated in FIG. 1A can be received by the computing units in the respective four columns in the processor array. Upon receiving the input signals X₁-X₄, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The four summing processors can output the four signals Y₁-Y₄ each combined with the weighted signals output from the computing units in a corresponding one of the four rows in the processor array.

Referring to FIG. 1A, after the wave-front multiplexer 213 outputs the signals Y₁, Y₂, Y₃ and Y₄, the signals Y₁, Y₂, Y₃ and Y₄ are transmitted in parallel into four inputs 4 a, 4 b, 4 c and 4 d of the four signal processing units or devices 999 a, 999 b, 999 c and 999 d and are processed by the signal processing units or devices 999 a, 999 b, 999 c and 999 d. The four signal processing units or devices 999 a, 999 b, 999 c and 999 d can be, but not limited to, four linear processors, four analog-to-digital (A/D) converters, four digital-to-analog (D/A) converters, four power amplifiers (PAs), four digital signal processors (DSPs), four chip packages, four integrated circuit (IC) chips, four system-on chips, four central processing units (CPUs), or four satellite transponders. Next, the four signal processing units or devices 999 a, 999 b, 999 c and 999 d output the processed signals, represented by four signals S₁, S₂, S₃ and S₄, in parallel from their outputs 5 a, 5 b, 5 c and 5 d. Next, the four signals S₁, S₂, S₃ and S₄ are transmitted in parallel to the four inputs 6 a, 6 b, 6 c and 6 d of the wave-front demultiplexer 232. The signal S₁ output from the output 5 a of the unit or device 999 a is correspondent to and processed based on the signal Y₁ output from the output 3 a of the wave-front multiplexer 213. The signal S₂ output from the output 5 b of the unit or device 999 b is correspondent to and processed based on the signal Y₂ output from the output 3 b of the wave-front multiplexer 213. The signal S₃ output from the output 5 c of the unit or device 999 c is correspondent to and processed based on the signal Y₃ output from the output 3 c of the wave-front multiplexer 213. The signal S₄ output from the output 5 d of the unit or device 999 d is correspondent to and processed based on the signal Y₄ output from the output 3 d of the wave-front multiplexer 213.

After the four signals S₁, S₂, S₃ and S₄ input in parallel to the four inputs 6 a, 6 b, 6 c and 6 d of the wave-front demultiplexer 232, the wave-front demultiplexer 232 performs the wave-front demultiplexing transform to multiply the four input signals S₁, S₂, S₃ and S₄, represented by a 4×1 input matrix D, by an orthogonal 4×4 matrix E so as to obtain four output signals Z₁, Z₂, Z₃ and Z₄ represented by a 4×1 output matrix F and then outputs the four output signals Z₁, Z₂, Z₃ and Z₄ from its outputs 7 a, 7 b, 7 c and 7 d. The matrix E is a square matrix, and the transpose of the matrix E is equal to the inverse of the matrix E. The below formula (2) illustrates the input matrix D multiplied by the orthogonal matrix E, performed on the wave-front demultiplexer 232.

$\begin{matrix} {{{{matrix}\mspace{14mu} D} = \begin{bmatrix} S_{1} \\ S_{2} \\ S_{3} \\ S_{4} \end{bmatrix}}{{{matrix}\mspace{14mu} E} = \begin{bmatrix} D_{11} & D_{12} & D_{13} & D_{14} \\ D_{21} & D_{22} & D_{23} & D_{24} \\ D_{31} & D_{32} & D_{33} & D_{34} \\ D_{41} & D_{42} & D_{43} & D_{44} \end{bmatrix}}{{{matrix}\mspace{14mu} F} = {{\begin{bmatrix} {{D_{11}S_{1}} + {D_{12}S_{2}} + {D_{13}S_{3}} + {D_{14}S_{4}}} \\ {{D_{21}S_{1}} + {D_{22}S_{2}} + {D_{23}S_{3}} + {D_{24}S_{4}}} \\ {{D_{31}S_{1}} + {D_{32}S_{2}} + {D_{33}S_{3}} + {D_{34}S_{4}}} \\ {{D_{41}S_{1}} + {D_{42}S_{2}} + {D_{43}S_{3}} + {D_{44}S_{4}}} \end{bmatrix}\begin{bmatrix} D_{11} & D_{12} & D_{13} & D_{14} \\ D_{21} & D_{22} & D_{23} & D_{24} \\ D_{31} & D_{32} & D_{33} & D_{34} \\ D_{41} & D_{42} & D_{43} & D_{44} \end{bmatrix}}{\quad{\begin{bmatrix} S_{1} \\ S_{2} \\ S_{3} \\ S_{4} \end{bmatrix} = {\begin{bmatrix} {{D_{11}S_{1}} + {D_{12}S_{2}} + {D_{13}S_{3}} + {D_{14}S_{4}}} \\ {{D_{21}S_{1}} + {D_{22}S_{2}} + {D_{23}S_{3}} + {D_{24}S_{4}}} \\ {{D_{31}S_{1}} + {D_{32}S_{2}} + {D_{33}S_{3}} + {D_{34}S_{4}}} \\ {{D_{41}S_{1}} + {D_{42}S_{2}} + {D_{43}S_{3}} + {D_{44}S_{4}}} \end{bmatrix} = \begin{bmatrix} Z_{1} \\ Z_{2} \\ Z_{3} \\ Z_{4} \end{bmatrix}}}}}}} & (2) \end{matrix}$

The components associated with the input S₁ in the four outputs are in the forms of D₁₁S₁, D₂₁S₁, D₃₁S₁ and D₄₁S₁. The weighting distribution of the components associated with the input S₁ in the four outputs is characterized by a first column vector, i.e. first wave-front demultiplexing vector (WFDV1), where

${{WFDV}\; 1} = \begin{bmatrix} D_{11} \\ D_{21} \\ D_{31} \\ D_{41} \end{bmatrix}$

Similarly, the components associated with the input S₂ in the four outputs are in the forms of D₁₂S₂, D₂₂S₂, D₃₂S₂ and D₄₂S₂. The weighting distribution of the components associated with the input S₂ in the four outputs is characterized by a second column vector, i.e. second wave-front demultiplexing vector (WFDV2), where

${{WFDV}\; 2} = \begin{bmatrix} D_{12} \\ D_{22} \\ D_{32} \\ D_{42} \end{bmatrix}$

The components associated with the input S₃ in the four outputs are in the forms of D₁₃S₃, D₂₃S₃, D₃₃S₃ and D₄₃S₃. The weighting distribution of the components associated with the input S₃ in the four outputs is characterized by a third column vector, i.e. third wave-front demultiplexing vector (WFDV3), where

${{WFDV}\; 3} = \begin{bmatrix} D_{13} \\ D_{23} \\ D_{33} \\ D_{43} \end{bmatrix}$

The components associated with the input S₄ in the four outputs are in the forms of D₁₄S₄, D₂₄S₄, D₃₄S₄ and D₄₄S₄. The weighting distribution of the components associated with the input S₄ in the four outputs is characterized by a fourth column vector, i.e. fourth wave-front demultiplexing vector (WFDV4), where

${{WFDV}\; 4} = \begin{bmatrix} D_{14} \\ D_{24} \\ D_{34} \\ D_{44} \end{bmatrix}$

The first and second wave-front demultiplexing vectors are mutually orthogonal to each other. The first and third wave-front demultiplexing vectors are mutually orthogonal to each other. The first and fourth wave-front demultiplexing vectors are mutually orthogonal to each other. The second and third wave-front demultiplexing vectors are mutually orthogonal to each other. The second and fourth wave-front demultiplexing vectors are mutually orthogonal to each other. The third and fourth wave-front demultiplexing vectors are mutually orthogonal to each other.

The output signal Z₁ is a linear combination, i.e. weighted sum, of all input signals S₁, S₂, S₃ and S₄ multiplied by the weightings D₁₁, D₁₂, D₁₃, and D₁₄, respectively. That is, the output signal Z₁ can be represented by a linear combination of D₁₁S₁ plus D₁₂S₂ plus D₁₃S₃ plus D₁₄S₄. The output signal Z₂ is a linear combination, i.e. weighted sum, of all input signals S₁, S₂, S₃ and S₄ multiplied by the weightings D₂₁, D₂₂, D₂₃, and D₂₄, respectively. That is, the output signal Z₂ can be represented by a linear combination of D₂₁S₁ plus D₂₂S₂ plus D₂₃S₃ plus D₂₄S₄. The output signal Z₃ is a linear combination, i.e. weighted sum, of all input signals S₁, S₂, S₃ and S₄ multiplied by the weightings D₃₁, D₃₂, D₃₃, and D₃₄, respectively. That is, the output signal Z₃ can be represented by a linear combination of D₃₁S₁ plus D₃₂S₂ plus D₃₃S₃ plus D₃₄S₄. The output signal Z₄ is a linear combination, i.e. weighted sum, of all input signals S₁, S₂, S₃ and S₄ multiplied by the weightings D₄₁, D₄₂, D₄₃, and D₄₄, respectively. That is, the output signal Z₄ can be represented by a linear combination of D₄₁S₁ plus D₄₂S₂ plus D₄₃S₃ plus D₄₄S₄.

Therefore, each of the output signals Z₁, Z₂, Z₃ and Z₄ output from the wave-front demultiplexer 232 is a linear combination, i.e. weighted sum, of all input signals S₁, S₂, S₃ and S₄ multiplied by respective weightings, and distributions of the weightings of any two input components in the four output signals are orthogonal. The weightings include D₁₁, D₁₂, D₁₃ and D₁₄ for the input signals S₁, S₂, S₃ and S₄, respectively, in the output signal Z₁, include D₂₁, D₂₂, D₂₃ and D₂₄ for the input signals S₁, S₂, S₃ and S₄, respectively, in the output signal Z₂, include D₃₁, D₃₂, D₃₃ and D₃₄ for the input signals S₁, S₂, S₃ and S₄, respectively, in the output signal Z₃, and include D₄₁, D₄₂, D₄₃ and D₄₄ for the input signals S₁, S₂, S₃ and S₄, respectively, in the output signal Z₄.

In other words, each of the output signals Z₁, Z₂, Z₃ and Z₄ is processed by multiple factors including the input signals S₁, S₂, S₃ and S₄ and the corresponding weightings. For the output signal Z₁, the factors include the input signals S₁, S₂, S₃ and S₄ and the weightings D₁₁, D₁₂, D₁₃ and D₁₄. For the output signal Z₂, the factors include the input signals S₁, S₂, S₃ and S₄ and the weightings D₂₁, D₂₂, D₂₃ and D₂₄. For the output signal Z₃, the factors include the input signals S₁, S₂, S₃ and S₄ and the weightings D₃₁, D₃₂, D₃₃ and D₃₄. For the output signal Z₄, the factors include the input signals S₁, S₂, S₃ and S₄ and the weightings D₄₁, D₄₂, D₄₃ and D₄₄.

Therefore, each of the signals Z₁, Z₂, Z₃ and Z₄ output from the wave-front multiplexer 232 is correspondent to or carries information associated with one of the signal X₁, X₂, X₃ and X₄ input to the wave-front multiplexer 213.

The matrix B and the matrix E, for example, can be equal. That is, the weightings at the same column and row in the matrix B and the matrix E have the same values, and the matrix B has the same number of rows and columns as the matrix E. In other words, the matrix B and the matrix E have the same dimensions and have the same values at the same positions. For instance, the weighting C₁₁ of the matrix B may have a value equal to the value of the weighting D₁₁ of the matrix E. The weighting C₁₂ of the matrix B may have a value equal to the value of the weighting D₁₂ of the matrix E. The weighting C₁₃ of the matrix B may have a value equal to the value of the weighting D₁₃ of the matrix E. The weighting C₁₄ of the matrix B may have a value equal to the value of the weighting D₁₄ of the matrix E. The weighting C₂₁ of the matrix B may have a value equal to the value of the weighting D₂₁ of the matrix E. The weighting C₂₂ of the matrix B may have a value equal to the value of the weighting D₂₂ of the matrix E. The weighting C₂₃ of the matrix B may have a value equal to the value of the weighting D₂₃ of the matrix E. The weighting C₂₄ of the matrix B may have a value equal to the value of the weighting D₂₄ of the matrix E. The weighting C₃₁ of the matrix B may have a value equal to the value of the weighting D₃₁ of the matrix E. The weighting C₃₂ of the matrix B may have a value equal to the value of the weighting D₃₂ of the matrix E. The weighting C₃₃ of the matrix B may have a value equal to the value of the weighting D₃₃ of the matrix E. The weighting C₃₄ of the matrix B may have a value equal to the value of the weighting D₃₄ of the matrix E. The weighting C₄₁ of the matrix B may have a value equal to the value of the weighting D₄₁ of the matrix E. The weighting C₄₂ of the matrix B may have a value equal to the value of the weighting D₄₂ of the matrix E. The weighting C₄₃ of the matrix B may have a value equal to the value of the weighting D₄₃ of the matrix E. The weighting C₄₄ of the matrix B may have a value equal to the value of the weighting D₄₄ of the matrix E.

Alternatively, the matrix E can be constructed to be equal to the matrix B multiplied by a scalar, and the matrix B and the matrix E have the same dimensions. That is, each of the weightings D₁₁, D₁₂, D₁₃, D₁₄, D₂₁, D₂₂, D₂₃, D₂₄, D₃₁, D₃₂, D₃₃, D₃₄, D₄₁, D₄₂, D₄₃ and D₄₄ in the matrix E may have a value equal to the value of the corresponding one of the weightings C₁₁, C₁₂, C₁₃, C₁₄, C₂₁, C₂₂, C₂₃, C₂₄, C₃₁, C₃₂, C₃₃, C₃₄, C₄₁, C₄₂, C₄₃ and C₄₄ in the matrix B, at the same column and row as the each of the weightings D₁₁, D₁₂, D₁₃, D₁₄, D₂₁, D₂₂, D₂₃, D₂₄, D₃₁, D₃₂, D₃₃, D₃₄, D₄₁, D₄₂, D₄₃ and D₄₄ in the matrix E, multiplied by the same scalar, and the matrix B has the same numbers of rows and columns as the matrix E. The weightings D₁₁, D₁₂, D₁₃, D₁₄, D₂₁, D₂₂, D₂₃, D₂₄, D₃₁, D₃₂, D₃₃, D₃₄, D₄₁, D₄₂, D₄₃ and D₄₄ in the matrix E may have values equal respectively to the values of the corresponding weightings C₁₁, C₁₂, C₁₃, C₁₄, C₂₁, C₂₂, C₂₃, C₂₄, C₃₁, C₃₂, C₃₃, C₃₄, C₄₁, C₄₂, C₄₃ and C₄₄ in the matrix B multiplied by the same scalar.

Alternatively, each weighting in the matrix E may have a value taking the complex conjugate of the value of the corresponding weighting in the matrix B, at the same column and row as the each weighting in the matrix E. For instance, the weighting C₁₁ of the matrix B has a value equal to the conjugate of the value of the weighting D₁₁. The weighting C₁₂ of the matrix B has a value equal to the conjugate of the value of the weighting D₁₂. The weighting C₁₃ of the matrix B has a value equal to the conjugate of the value of the weighting D₁₃. The weighting C₁₄ of the matrix B has a value equal to the conjugate of the value of the weighting D₁₄. The weighting C₂₁ of the matrix B has a value equal to the conjugate of the value of the weighting D₂₁. The weighting C₂₂ of the matrix B has a value equal to the conjugate of the value of the weighting D₂₂. The weighting C₂₃ of the matrix B has a value equal to the conjugate of the value of the weighting D₂₃. The weighting C₂₄ of the matrix B has a value equal to the conjugate of the value of the weighting D₂₄. The weighting C₃₁ of the matrix B has a value equal to the conjugate of the value of the weighting D₃₁. The weighting C₃₂ of the matrix B has a value equal to the conjugate of the value of the weighting D₃₂. The weighting C₃₃ of the matrix B has a value equal to the value of the conjugate of the weighting D₃₃. The weighting C₃₄ of the matrix B has a value equal to the conjugate of the value of the weighting D₃₄. The weighting C₄₁ of the matrix B has a value equal to the conjugate of the value of the weighting D₄₁. The weighting C₄₂ of the matrix B has a value equal to the conjugate of the value of the weighting D₄₂. The weighting C₄₃ of the matrix B has a value equal to the conjugate of the value of the weighting D₄₃. The weighting C₄₄ of the matrix B has a value equal to the conjugate of the value of the weighting D₄₄.

Alternatively, each of the weightings D₁₁, D₁₂, D₁₃, D₁₄, D₂₁, D₂₂, D₂₃, D₂₄, D₃₁, D₃₂, D₃₃, D₃₄, D₄₁, D₄₂, D₄₃ and D₄₄ in the matrix E may have a value taking the complex conjugate of the value of the corresponding one of the weightings C₁₁, C₁₂, C₁₃, C₁₄, C₂₁, C₂₂, C₂₃, C₂₄, C₃₁, C₃₂, C₃₃, C₃₄, C₄₁, C₄₂, C₄₃ and C₄₄ in the matrix B, at the same column and row as the each of the weightings D₁₁, D₁₂, D₁₃, D₁₄, D₂₁, D₂₂, D₂₃, D₂₄, D₃₁, D₃₂, D₃₃, D₃₄, D₄₁, D₄₂, D₄₃ and D₄₄ in the matrix E, multiplied by the same scalar, and the matrix B has the same numbers of rows and columns as the matrix E. The weightings D₁₁, D₁₂, D₁₃, D₁₄, D₂₁, D₂₂, D₂₃, D₂₄, D₃₁, D₃₂, D₃₃, D₃₄, D₄₁, D₄₂, D₄₃ and D₄₄ in the matrix E may have values equal respectively to the conjugates of the values of the weightings C₁₁, C₁₂, C₁₃, C₁₄, C₂₁, C₂₂, C₂₃, C₂₄, C₃₁, C₃₂, C₃₃, C₃₄, C₄₁, C₄₂, C₄₃ and C₄₄ in the matrix B multiplied by the same scalar.

Referring to FIG. 1E showing architecture of a wave-front demultiplexer in accordance with the present invention. For more elaboration, the wave-front demultiplexer can be adapted to receive the number I of input signals S, process the number I of the input signals S to be multiplied by the above-mentioned WFDM matrix, such as I-by-I square orthogonal matrix, and output the number I of output signals Z, wherein I could be any number greater than or equal to 2, 4, 8, 16, 32, 64, 126 or 256. The input signals S can be, but not limited to, analog or digital signals. The output signals Z can be, but not limited to, analog or digital signals. The wave-front demultiplexer may include the number I*I of computing units and the number I of summing processors. The computing units form an I-by-I processor array with the number I of columns and the number I of rows. The computing units in each column in the processor array receive a corresponding input signal S, and thus the number I of the input signals S can be received by the computing units in the number I of the respective columns in the processor array. Upon receiving the input signals S, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. Each of the summing processors provides a means for summing weighted signals generated by the corresponding computing units in same row in the processor array to produce a corresponding output signal Z. Accordingly, the number I of the summing processors can output the number I of the output signals Z each combined with the weighted signals output from the computing units in a corresponding one of the number I of the rows in the processor array. The above-mentioned description of the wave-front demultiplexer can be applied to the following embodiments.

In the case illustrated in FIG. 1A, the number of I is equal to 4. The wave-front demultiplexer 232 illustrated in FIG. 1A may include 4*4 computing units and four summing processors. The computing units form a processor array with four rows and four columns. The four input signals S₁-S₄ illustrated in FIG. 1A can be received by the computing units in the respective four columns in the processor array. Upon receiving the four input signals S₁-S₄, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The four summing processors can output the four signals Z₁-Z₄ each combined with the weighted signals output from the computing units in a corresponding one of the four rows in the processor array.

Referring to FIGS. 1A, 1D and 1E, when the above-mentioned wave-front demultiplexing transformation performed by the wave-front demultiplexer 232 having the architecture illustrated in FIG. 1E inverts or transforms signals previously transformed by the wave-front multiplexing transformation performed by its complementary wave-front multiplexer 213 having the architecture illustrated in FIG. 1D, the number of H is equal to the number of I. Each weighting for multiplying a corresponding one of the input signals X, performed by a corresponding one of the computing units of the wave-front multiplexer 213, may have the same value as the corresponding weighting for multiplying a corresponding one of the input signals S, performed by a corresponding one of the computing units of the wave-front demultiplexer 232 at the same row and column as the corresponding computing unit of the wave-front multiplexer 213. Alternatively, each weighting for multiplying a corresponding one of the input signals X, performed by a corresponding one of the computing units of the wave-front multiplexer 213, may have a value equal to that of the corresponding weighting for multiplying a corresponding one of the input signals S, performed by a corresponding one of the computing units of the wave-front demultiplexer 232 at the same row and column as the corresponding computing unit of the wave-front multiplexer 213, multiplied by the same scalar. Alternatively, each weighting for multiplying a corresponding one of the input signals X, performed by a corresponding one of the computing units of the wave-front multiplexer 213, may have a value equal to the conjugate of the value of the corresponding weighting for multiplying a corresponding one of the input signals S, performed by a corresponding one of the computing units of the wave-front demultiplexer 232 at the same row and column as the corresponding computing unit of the wave-front multiplexer 213. Alternatively, each weighting for multiplying a corresponding one of the input signals X, performed by a corresponding one of the computing units of the wave-front multiplexer 213, may have a value equal to the conjugate of the value of the corresponding weighting for multiplying a corresponding one of the input signals S, performed by a corresponding one of the computing units of the wave-front demultiplexer 232 at the same row and column as the corresponding computing unit of the wave-front multiplexer 213, multiplied by the same scalar.

Alternatively, referring to FIG. 1B, the system 888 may further include an equalizer or equalization processor 231 and an optimizer or optimization processor 235 for performing signal compensations. The system 200 shown in FIG. 1B is similar to the system 200 illustrated in FIG. 1A except that the system 200 illustrated in FIG. 1B further includes the equalizer 231 and the optimizer 235 and that the signal X₄ illustrated in FIG. 1A is replaced with a pilot or diagnostic signal X₄ shown in FIG. 1B. The pilot or diagnostic signal X₄ may have a single frequency and fixed amplitude. Alternatively, the pilot or diagnostic signal X₄ could change based on time or could be any signal known by the system 888. In contrast, the extraneous signals X₁, X₂ and X₃ are unknown by the system 888 and input into the system 888 from an extraneous system.

Besides, compared with the signals S₁, S₂, S₃ and S₄, in FIG. 1A, input into the wave-front demultiplexer 232, the signals S₁, S₂, S₃ and S₄, in FIG. 1B, are equalized by the equalizer 231. In this embodiment, four signals W₁, W₂, W₃ and W₄ are defined as ones output from outputs 5 a, 5 b, 5 c and 5 d of the four signal processing units or device 999 a, 999 b, 999 c and 999 d and have not been equalized by the equalizer 231.

The signal processing unit or device 999 a is in a first signal path between the output 3 a of the wave-front multiplexer 213 and an input 10 a of the equalizer 231, being used to process an input signal, such as the signal Y₁ output from the output 3 a, so as to output another signal, such as the signal W₁. The signal processing unit or device 999 b is in a second signal path between the output 3 b of the wave-front multiplexer 213 and an input 10 b of the equalizer 231, being used to process an input signal, such as the signal Y₂ output from the output 3 b, so as to output another signal, such as the signal W₂. The signal processing unit or device 999 c is in a third signal path between the output 3 c of the wave-front multiplexer 213 and an input 10 c of the equalizer 231, being used to process an input signal, such as the signal Y₃ output from the output 3 c, so as to output another signal, such as the signal W₃. The signal processing unit or device 999 d is in a fourth signal path between the output 3 d of the wave-front multiplexer 213 and an input 10 d of the equalizer 231, being used to process an input signal, such as the signal Y₄ output from the output 3 d, so as to output another signal, such as the signal W₄. The first, second, third and fourth signal paths are arranged in parallel.

The equalizer 231 is in four signal paths between the four outputs 5 a, 5 b, 5 c and 5 d of the four signal processing units or devices 999 a, 999 b, 999 c and 999 d and the input ports 6 a, 6 b, 6 c and 6 d of the wave-front demultiplexer 232. The optimizer 235 is in a signal path between the equalizer 231 and the outputs 7 a, 7 b, 7 c and 7 d of the wave-front demultiplexer 232. In this embodiment, the input signal X₄ input to the input 2 d of the wave-front multiplexer 213 is a pilot or diagnostic signal. The output signal Z₄ output from the output 7 d of the wave-front demultiplexer 232 is also a pilot or diagnostic signal correspondent to or carries information associated with the input signal X₄. The equalizer 231 can perform amplitude, phase, and time-delay compensation to adjust the amplitudes, phases, and/or time-delays of the signals W₁, W₂, W₃ and W₄. The wave-front multiplexing transform performed by the wave-front multiplexer 213 shown in FIG. 1B can be referred to as the wave-front multiplexing transform performed by the wave-front multiplexer 213 as illustrated in FIG. 1A. The wave-front demultiplexing transform performed by the wave-front demultiplexer 232 shown in FIG. 1B can be referred to as the wave-front demultiplexing transform performed by the wave-front demultiplexer 232 as illustrated in FIG. 1A.

To avoid propagation effects and/or the difference of unbalanced amplitudes, unbalanced phases and/or unbalanced time-delays among the signals W₁, W₂, W₃ and W₄ output from the units or devices 999 a, 999 b, 999 c and 999 d, the system 888 performs an optimizing and equalizing process to the signals W₁, W₂, W₃ and W₄ by the equalizer 231 and the optimization processor 235. After inputting the signals W₁, W₂, W₃ and W₄ to the inputs 10 a, 10 b, 10 c and 10 d of the equalizer 231, the equalizer 231 generates the corresponding equalized signals S₁, S₂, S₃ and S₄ according to a control signal CS output from the optimization processor 235, wherein the corresponding equalized signals S₁, S₂, S₃ and S₄ are output from its outputs 11 a, 11 b, 11 c and 11 d, respectively.

During the optimizing and equalizing process, a cost function may be used to measure the difference between the diagnostic input 2 d of the wave-front multiplexer 213 and the diagnostic output 7 d of the wave-front demultiplexer 232. Then, the system 888 uses the optimization processor 235 to generate the control signal CS which can be used to adjust the equalizer 231 in order to minimize the cost function. Then, an adaptive equalization is reached when the cost function is minimal and the cost function can no longer be reduced any further. The processors 231 and 235 can perform an amplitude, phase, and/or time-delay compensation.

FIG. 1C shows a flow chart of an optimizing and equalizing process performed by a system, which can be applied to all of the embodiments of the present disclosure. Referring to FIG. 1C, in step 401, an optimizer, such as the optimizer 235, e.g., illustrated in FIG. 1B, can be configured to receive one or some of output diagnostic signals from one or some of output ports of a wave-front demultiplexer such as the wave-front demultiplexer 232, e.g., illustrated in FIG. 1B. For example, the optimizer 235, e.g., illustrated in FIG. 1B can be configured to receive the signal Z₄ from the output port 7 d of the wave-front demultiplexer 232. Alternatively, the optimizer may be configured to receive the signals from all of the output ports of the wave-front demultiplexer. For example, the optimizer 235, e.g., illustrated in FIG. 1B may be configured to receive the signals Z₁, Z₂, Z₃ and Z₄ from the output ports 7 a, 7 b, 7 c and 7 d of the wave-front demultiplexer 232.

Next, in step 402, the optimizer is configured to calculate one or some differences between values represented by the output diagnostic signals, such as the signal Z₄, e.g., illustrated in FIG. 1B, and corresponding predetermined values known by the system such as the system 888 illustrated in FIG. 1B, wherein one or some input diagnostic signals, such as the signal X₄, e.g., illustrated in FIG. 1B, input into a corresponding or complementary wave-front multiplexer, such as the wave-front multiplexer 213, e.g., illustrated in FIG. 1B, at the same sequences as the corresponding output diagnostic signals, such as the signal Z₄, e.g., illustrated in FIG. 1B, represent the predetermined values. Alternatively, the optimizer may be configured further to calculate a correlation between each two of the signals from all of the output ports of the wave-front demultiplexer in case that all of the signals from the output ports of the wave-front demultiplexer are received by the optimizer. For example, the optimizer 235, e.g., illustrated in FIG. 1B may be configured further to calculate correlations between the signals Z₁ and Z₂, between the signals Z₁ and Z₃, between the signals Z₁ and Z₄, between the signals Z₂ and Z₃, between the signals Z₂ and Z₄, and the signals Z₃ and Z₄ in case that all of the signals Z₁, Z₂, Z₃ and Z₄ output from the output ports 7 a, 7 b, 7 c and 7 d of the wave-front demultiplexer 232 are received by the optimizer 235.

Next, in step 403, the optimizer is configured to calculate a sum value, i.e. cost, by performing weighted summation of multiple factors including the differences. Alternatively, the factors may further include the correlations in case that the correlations are obtained.

Next, in step 404, the optimizer is configured to compare the calculated sum value or cost with a threshold sum value, i.e. threshold cost.

In step 405, the optimizer is configured to calculate a variation in the calculated sum value or cost in response to finding the calculated sum value or cost is greater than the threshold sum value or threshold cost.

After calculating the variation in step 405, step 406 is performed with the optimizer creating one or more control signals, such as the control signal CS, e.g., shown in FIG. 1B, based on the variation and sending the control signals to an equalizer, such as the equalizer 231, e.g., illustrated in FIG. 1B, so as to adjust the values of weightings of the equalizer.

In step 407, after the weightings are adjusted based on the control signals, the equalizer can equalize the received signals, such as the signals W₁, W₂, W₃ and W₄, e.g., illustrated in FIG. 1B, based on the adjusted weightings so as to output the equalized signals, such as the equalized signals S₁, S₂, S₃ and S₄, e.g., illustrated in FIG. 1B, into the wave-front demultiplexer. For example, the equalized signal S₁, e.g., illustrated in FIG. 1B is created by the equalizer 231 multiplying the signal W₁ by a weighting of the equalizer 231. The equalized signal S₂, e.g., illustrated in FIG. 1B is created by the equalizer 231 multiplying the signal W₂ by another weighting of the equalizer 231. The equalized signal S₃, e.g., illustrated in FIG. 1B is created by the equalizer 231 multiplying the signal W₃ by another weighting of the equalizer 231. The equalized signal S₄, e.g., illustrated in FIG. 1B is created by the equalizer 231 multiplying the signal W₄ by the other weighting of the equalizer 231.

Each of the weightings of the equalizer can be, but not limited to, a complex value such that the equalized signals, such as the equalized signals S₁, S₂, S₃ and S₄, e.g., illustrated in FIG. 1B, can be rotated precisely to become in phase. In case that the equalizer is performed by a narrow band equalizer, such as amplitude-and-phase filter, the narrow band equalizer can alter each of the received signals, such as the signals W₁, W₂, W₃ and W₄, e.g., illustrated in FIG. 1B, of the equalizer by amplitude and phase amounts fixed across a narrow frequency band. The narrow band equalizer can provide phase and amplitude modifications to each of the received signals, such as the signals W₁, W₂, W₃ and W₄, e.g., illustrated in FIG. 1B, of the equalizer featuring a constant phase shift and a constant amplitude attenuation across the narrow frequency band. Alternatively, in case that the equalizer is performed by a broadband equalizer, such as finite impulse filter (FIR), the broadband equalizer can alter each of the received signals, such as the signals W₁, W₂, W₃ and W₄, e.g., illustrated in FIG. 1B, of the equalizer by amplitude and phase amounts depending on an amplitude and phase profile, changing with frequencies, across a broad frequency band. The broad band equalizer can provide phase and amplitude modifications to each of the received signals, such as the signals W₁, W₂, W₃ and W₄, e.g., illustrated in FIG. 1B, of the equalizer featuring a constant phase shift and a constant amplitude attenuation in each sub-band across the broad frequency band, but the phase shift and amplitude attenuation in one sub-band across the broad frequency band is different from those in the other sub-bands across the broad frequency band.

Next, in step 408, the equalized signals, such as the equalized signals S₁, S₂, S₃ and S₄, e.g., illustrated in FIG. 1B, are transformed into multiple linear combinations by the wave-front demultiplexer performing the above-mentioned wave-front demultiplexing transformation, wherein each linear combination is combined with the equalized signals, such as the equalized signals S₁, S₂, S₃ and S₄, e.g., illustrated in FIG. 1B, multiplied by respective weightings of the wave-front demultiplexer, represented by the signals, such as the signals Z₁, Z₂, Z₃ and Z₄, e.g., illustrated in FIG. 1B, output in parallel from the output ports of the wave-front demultiplexer.

Next, step 401 is performed again so as to form the above loop of steps 401-408, as seen in FIG. 1C. In step 409, the optimizer is configured to stop the above loop in response to finding the calculated sum value or cost is less than the threshold sum value or threshold cost. Therefore, the equalizer coupled to the optimizer can dynamically provide a compensation function to compensate the received signals, such as the signals W₁, W₂, W₃ and W₄, e.g., illustrated in FIG. 1B, of the equalizer for propagation effects and/or difference of unbalanced amplitudes, unbalanced phases, and/or unbalanced time-delays so as to improve the signals, such as the signals Z₁, Z₂, Z₃ and Z₄, e.g., illustrated in FIG. 1B, output from the wave-front demultiplexer.

In all of the embodiments of the present disclosure, the equalizer, the wave-front demultiplexer and the optimizer can be, but not limited to, embedded in a processor, such as single integrated circuit chip, single system-on chip or single chip package. The equalizer can be hardware or can be realized by software installed in and performed by the processor. The optimizer can be hardware or can be realized by software installed in and performed by the processor.

The above-mentioned descriptions of the wave-front multiplexer, the wave-front demultiplexer, the equalizer, and the optimizer can be applied to the following embodiments.

First Embodiment: Application to Analog-to-Digital Converter

FIG. 2A shows a system for converting analog signals into digital signals constructed with digital representation of the analog signals using a wave-front multiplexer, multiple analog-to-digital converters and a wave-front demultiplexer according to an exemplary embodiment of the present disclosure.

Referring to FIG. 2A, an analog-to-digital (A/D) conversion system 200 may include a wave-front multiplexer 213, four individual analog-to-digital converters (or called ADCs or A/D converters) 220 a, 220 b, 220 c and 220 d, and a wave-front demultiplexer 232. In this embodiment, the four processing units or devices 999 a, 999 b, 999 c and 999 d as illustrated in FIG. 1A can be replaced with the four analog-to-digital converters 220 a, 220 b, 220 c and 220 d illustrated in FIG. 2A.

The wave-front multiplexer 213 can receive, in parallel, four individual and independent analog signals X₁, X₂, X₃ and X₄, processes all the analog signals X₁, X₂, X₃ and X₄ into four analog signals Y₁, Y₂, Y₃ and Y₄ by the above-mentioned wave-front multiplexing transform, and outputs the analog signals Y₁, Y₂, Y₃ and Y₄ in parallel, which can be referred to as the description illustrated in FIG. 1A. Each of the analog signals Y₁, Y₂, Y₃ and Y₄ is a linear combination, i.e. weighted sum, of all the analog signals X₁, X₂, X₃ and X₄ multiplied by respective weightings, and distributions of the weightings of any two input components in all analog signals Y₁, Y₂, Y₃ and Y₄ are orthogonal, which can be referred to as the description illustrated in FIGS. 1A and 1D. In this case, the number of H is equal to 4. The wave-front multiplexer 213 may include 4*4 computing units and four summing processors. The computing units form a processor array with four rows and four columns. The input signals X₁-X₄ can be received by the computing units in the respective four columns in the processor array. Upon receiving the input signals X₁-X₄, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The four summing processors can output the four signals Y₁-Y₄ each combined with the weighted signals output from the computing units in a corresponding one of the four rows in the processor array.

The wave-front multiplexer 213 can be, but not limited to, embedded in a processor. The wave-front multiplexer 213 can be, but not limited to, hardware, such as four-by-four Butler matrix or a device performing any transformation of a four-by-four orthogonal matrix.

The wave-front multiplexer 213 can be a multiple-input and multiple-output (MIMO) one that has at least as many output signal paths as there exist input signal paths connected to the wave-front multiplexer 213. For example, the wave-front multiplexer 213 may have four input ports (i.e. inputs) 2 a, 2 b, 2 c and 2 d that are arranged in parallel and available to receiving the analog signals X₁, X₂, X₃ and X₄ passing in parallel through four parallel input channels, and four output ports (i.e. outputs) 3 a, 3 b, 3 c and 3 d that are arranged in parallel and available to outputting the analog signals Y₁, Y₂, Y₃ and Y₄ passing in parallel through four parallel output channels.

Alternatively, the wave-front multiplexer 213 can be applied for processing or calculating for multiple linear combinations to multiple analog input signals, passing in parallel through parallel input channels, received by multiple parallel input ports of the wave-front multiplexer 213 so as to output multiple analog output signals in parallel from multiple parallel output ports of the wave-front multiplexer 213, and then the analog output signals pass in parallel through parallel output channels coupled to the parallel output ports of the wave-front multiplexer 213 and to multiple parallel input ports of multiple analog-to-digital converters. The total number of the parallel input ports of the wave-front multiplexer 213 may be equal to the total number of the parallel output ports of the wave-front multiplexer 213 and can be any number equal to or more than two, four, eight, sixteen or thirty-two. The total number of the parallel input channels is equal to the total number of the parallel output channels and can be any number equal to or more than two, four, eight, sixteen or thirty-two. The total number of the analog input signals to be processed or calculated in parallel by the wave-front multiplexer 213 for the above linear combinations can be equal to or less than the total number of the parallel input ports of the wave-front multiplexer 213 and can be any number equal to or more than two, four, eight, sixteen or thirty-two. The total number of the analog output signals, passing in parallel, processed or calculated by the wave-front multiplexer 213 for the above linear combinations can be equal to the total number of the parallel output ports and can be any number equal to or more than two, four, eight, sixteen or thirty-two. The total number of the analog-to-digital converters can be equal to or less than the total number of the analog output signals and can be any number equal to or more than two, four, eight, sixteen or thirty-two.

The wave-front demultiplexer 232 can receive, in parallel, multiple individual digital signals S₁, S₂, S₃ and S₄ output in parallel from the analog-to-digital converters 220 a, 220 b, 220 c and 220 d, extracts multiple coherently combined digital signals Z₁, Z₂, Z₃ and Z₄, which are digital representations of the analog signals X₁, X₂, X₃ and X₄, from the digital signals S₁, S₂, S₃ and S₄ by the above-mentioned wave-front demultiplexing transform, and outputs the digital signals Z₁, Z₂, Z₃ and Z₄ in parallel, which can be referred to as the description illustrated in FIG. 1A. Each of the digital signals Z₁, Z₂, Z₃ and Z₄ is a linear combination, i.e. weighted sum, of all the digital signals S₁, S₂, S₃ and S₄ multiplied by respective weightings, and distributions of the weightings of any two input components in all digital signals Z₁, Z₂, Z₃ and Z₄ are orthogonal, which can be referred to as the description illustrated in FIGS. 1A and 1E. In this case, the number of I is equal to 4. The wave-front demultiplexer 232 may include 4*4 computing units and four summing processors. The computing units form a processor array with four rows and four columns. The input signals S₁-S₄ can be received by the computing units in the respective four columns in the processor array. Upon receiving the input signals S₁-S₄, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The four summing processors can output the four signals Z₁-Z₄ each combined with the weighted signals output from the computing units in a corresponding one of the four rows in the processor array. Each of the digital signals Z₁, Z₂, Z₃ and Z₄ can be, but not limited to, an intermediate-frequency (IF) digital signal or a radio-frequency (RF) digital signal.

The wave-front demultiplexer 232 can be, but not limited to, embedded in a processor. The wave-front demultiplexer 232 can be hardware achieving the wave-front demultiplexing transform, such as IFFT chip, four-by-four Butler matrix, or a device performing inverse Fourier transformation, inverse discrete Fourier transformation, inverse Hartley transformation, Hadamard transformation, any other inverse Fourier-related transformation, or any transformation of a four-by-four orthogonal matrix. Alternatively, the function of the wave-front demultiplexer 232 can be realized by software installed in and performed by the processor, wherein the software can perform the above wave-front demultiplexing transform.

The wave-front demultiplexer 232 can be a multiple-input and multiple-output (MIMO) one that has at least as many parallel output channels as there exist parallel input channels connected to the wave-front demultiplexer 232. For example, the wave-front demultiplexer 232 may have four input ports (i.e. inputs) 6 a, 6 b, 6 c and 6 d that are arranged in parallel and available to receiving the digital signals S₁, S₂, S₃ and S₄ passing in parallel through four parallel input channels, and four output ports (i.e. outputs) 7 a, 7 b, 7 c and 7 d that are arranged in parallel and available to outputting the digital signals Z₁, Z₂, Z₃ and Z₄ passing in parallel through four parallel output channels.

Alternatively, the wave-front demultiplexer 232 can be applied for processing or calculating for multiple linear combinations to multiple digital input signals, output from multiple analog-to-digital converters, passing in parallel through parallel input channels, received by multiple parallel input ports of the wave-front demultiplexer 232 so as to output multiple digital output signals in parallel from multiple parallel output ports of the wave-front demultiplexer 232, and then the digital output signals pass in parallel through parallel output channels coupled to the output ports of the wave-front demultiplexer 232. The total number of the parallel input ports of the wave-front demultiplexer 232 may be equal to the total number of the parallel output ports of the wave-front demultiplexer 232 and can be any number equal to or more than two, four, eight, sixteen or thirty-two. The total number of the parallel input channels may be equal to the total number of the parallel output channels and can be any number equal to or more than two, four, eight, sixteen or thirty-two. The total number of the digital input signals to be processed or calculated in parallel by the wave-front demultiplexer 232 for the linear combinations can be equal to the total number of the parallel input ports of the wave-front demultiplexer 232 and can be any number equal to or more than two, four, eight, sixteen or thirty-two. The total number of the digital output signals, passing in parallel, processed or calculated by the wave-front demultiplexer 232 for the linear combinations can be equal to or less than the total number of the parallel output ports of the wave-front demultiplexer 232 and can be any number equal to or more than two, four, eight, sixteen or thirty-two. The total number of the analog-to-digital converters can be equal to or less than the total number of the digital input signals and can be any number equal to or more than two, four, eight, sixteen or thirty-two. The total number of the analog input signals input in parallel into the wave-front multiplexer 213 may be equal to the total number of the digital output signals output in parallel from the wave-front demultiplexer 232, and the digital output signals output in parallel from the wave-front demultiplexer 232 are digital representations of the analog input signals input in parallel into the wave-front multiplexer 213, respectively.

The four analog-to-digital converters 220 a, 220 b, 220 c and 220 d are arranged in four parallel signal paths between the wave-front multiplexer 213 and the wave-front demultiplexer 232 of the system 200. In other words, the analog-to-digital converter 220 a is arranged in a first signal path between the output port 3 a of the wave-front multiplexer 213 and the input port 6 a of the wave-front demultiplexer 232 of the system 200, and the first signal path includes the A/D converter 220 a, a signal path between the output port 3 a of the wave-front multiplexer 213 and the input port 4 a of the A/D converter 220 a, and a signal path between the output port 5 a of the A/D converter 220 a and the input port 6 a of the wave-front demultiplexer 232. The analog-to-digital converter 220 b is arranged in a second signal path between the output port 3 b of the wave-front multiplexer 213 and the input port 6 b of the wave-front demultiplexer 232 of the system 200, and the second signal path includes the A/D converter 220 b, a signal path between the output port 3 b of the wave-front multiplexer 213 and the input port 4 b of the A/D converter 220 b, and a signal path between the output port 5 b of the A/D converter 220 b and the input port 6 b of the wave-front demultiplexer 232. The analog-to-digital converter 220 c is arranged in a third signal path between the output port 3 c of the wave-front multiplexer 213 and the input port 6 c of the wave-front demultiplexer 232 of the system 200, and the third signal path includes the A/D converter 220 c, a signal path between the output port 3 c of the wave-front multiplexer 213 and the input port 4 c of the A/D converter 220 c, and a signal path between the output port 5 c of the A/D converter 220 c and the input port 6 c of the wave-front demultiplexer 232. The analog-to-digital converter 220 d is arranged in a fourth signal path between the output port 3 d of the wave-front multiplexer 213 and the input port 6 d of the wave-front demultiplexer 232 of the system 200, and the fourth signal path includes the A/D converter 220 d, a signal path between the output port 3 d of the wave-front multiplexer 213 and the input port 4 d of the A/D converter 220 d, and a signal path between the output port 5 d of the A/D converter 220 d and the input port 6 d of the wave-front demultiplexer 232.

Each of the analog-to-digital converters 220 a, 220 b, 220 c and 220 d can convert an analog signal into a digital representation of the analog signal. Each of the analog-to-digital converters 220 a, 220 b, 220 c and 220 d can be, but not limited to, a parallel-output analog-to-digital converter or a serial-output analog-to-digital converter. For instance, each of the analog-to-digital converters 220 a, 220 b, 220 c and 220 d can be a parallel-output one having an output port, such as output port 5 a, 5 b, 5 c or 5 d, with multiple parallel output nodes for outputting a digital representation of an analog signal, represented by the digital signal S₁, S₂, S₃ or S₄. The digital signals S₁, S₂, S₃ and S₄ passing in parallel can be transmitted to parallel input ports of a device or processor, such as the parallel input port 6 a, 6 b, 6 c or 6 d of the wave-front demultiplexer 232, through parallel channels (such as wireless channels or physical channels) coupled to the parallel output ports 5 a, 5 b, 5 c and 5 d, respectively, and to the parallel input ports of the device or processor, respectively.

Each of the analog-to-digital converters 220 a, 220 b, 220 c and 220 d, for example, may have the same sampling rate or sampling frequency, based on which analog-to-digital conversions are performed by the analog-to-digital converters 220 a, 220 b, 220 c and 220 d. Alternatively, each of the analog-to-digital converters 220 a, 220 b, 220 c and 220 d may have different sampling rates or sampling frequencies, based on which analog-to-digital conversions are performed by the analog-to-digital converters 220 a, 220 b, 220 c and 220 d.

Each of the analog-to-digital converters 220 a, 220 b, 220 c and 220 d, for example, may have the same analog-to-digital conversion resolution, based on which analog-to-digital conversions are performed by the analog-to-digital converters 220 a, 220 b, 220 c and 220 d. Alternatively, each of the analog-to-digital converters 220 a, 220 b, 220 c and 220 d may have different analog-to-digital conversion resolutions, based on which analog-to-digital conversions are performed by the analog-to-digital converters 220 a, 220 b, 220 c and 220 d.

Alternatively, multiple analog-to-digital converters arranged in parallel can be arranged in multiple parallel signal paths between the wave-front multiplexer 213 and the wave-front demultiplexer 232 of the system 200 and can perform analog-to-digital conversions to multiple analog signals, passing in parallel through multiple parallel channels and output from parallel output ports of the wave-front multiplexer 213, so as to convert the analog signals into multiple digital signals, respectively, which are digital representations of the analog signals. The total number of the analog-to-digital convertors processing the analog signals output in parallel from the wave-front multiplexer 213 may be equal to or less than the total number of the parallel output ports of the wave-front multiplexer 213, may be equal to or less than the total number of the parallel input ports of the wave-front de-multiplexer 232, and can be any number equal to or more than two, four, eight, sixteen or thirty-two.

The system 200 may further include four low pass filters, respectively, in four signal paths before the input ports 2 a, 2 b, 2 c and 2 d of the wave-front multiplexer 213. In other words, the four extraneous analog signals X₁, X₂, X₃ and X₄ may be output in parallel from the four low pass filters, respectively, such that each of the analog signals X₁, X₂, X₃ and X₄ has attenuated parts with frequencies higher than a cutoff frequency, and then the analog signals X₁, X₂, X₃ and X₄ are transmitted into the parallel input ports 2 a, 2 b, 2 c and 2 d of the wave-front multiplexer 213, respectively, through, e.g., four parallel channels, such as wireless channels or physical channels.

A method for processing signals or data streams by using the system 200 is described below. The individual analog signals X₁, X₂, X₃ and X₄ from, e.g., one or more wireless base stations or array elements such as antenna array elements are input in parallel to the input ports 2 a, 2 b, 2 c and 2 d of the wave-front multiplexer 213 through, e.g., four parallel signal paths, four parallel wireless channels or four parallel physical channels. Each of the wireless base stations can be, but not limited to, a mobile base station or a Wi-Fi base station. Alternatively, the analog signals X₁, X₂, X₃ and X₄ can come from, but not limited to, one or more microphone devices, one or more image sensors, one or more micro-electro-mechanical-system (MEMS) microphone chips, or one or more antennas of a mobile phone. After the analog signals X₁, X₂, X₃ and X₄ are input in parallel to the wave-front multiplexer 213, the wave-front multiplexer 213 performs the above-mentioned wave-front multiplexing transformation to process the individual analog signals X₁, X₂, X₃ and X₄ into four linear combinations, each combined with the analog signals X₁, X₂, X₃ and X₄ multiplied by respective weightings, represented by the analog signals Y₁, Y₂, Y₃ and Y₄. Next, the wave-front multiplexer 213 outputs the four analog signals Y₁, Y₂, Y₃ and Y₄ from the four output ports 3 a, 3 b, 3 c and 3 d, and the four analog signals Y₁, Y₂, Y₃ and Y₄ are transmitted into the four input ports 4 a, 4 b, 4 c and 4 d of the four analog-to-digital converters 220 a, 220 b, 220 c and 220 d, respectively, through, e.g., four parallel channels, such as wireless channels or physical channels.

After the analog signals Y₁, Y₂, Y₃ and Y₄ are transmitted in parallel into the analog-to-digital converters 220 a, 220 b, 220 c and 220 d arranged in parallel, the analog-to-digital converters 220 a, 220 b, 220 c and 220 d transform the analog signals Y₁, Y₂, Y₃ and Y₄ into digital representations of the analog signals Y₁, Y₂, Y₃ and Y₄, represented by the digital signals S₁, S₂, S₃ and S₄ respectively, and output the four digital signals S₁, S₂, S₃ and S₄ in parallel from the four output ports 5 a, 5 b, 5 c and 5 d of the analog-to-digital converters 220 a, 220 b, 220 c and 220 d. The analog signals Y₁, Y₂, Y₃ and Y₄ may be sampled at the same sampling frequency or at different sampling frequencies by the analog-to-digital converters 220 a, 220 b, 220 c and 220 d. The analog-to-digital converters 220 a, 220 b, 220 c and 220 d, for example, could be realized by four integrated circuit chips embedded in a single chip package, by four integrated circuit chips embedded in four individual chip packages, or by a single integrated circuit chip. Alternatively, the function of the analog-to-digital converters 220 a, 220 b, 220 c and 220 d can be realized by software installed in the system 200.

Next, the digital signals S₁, S₂, S₃ and S₄ are transmitted in parallel into the four input ports 6 a, 6 b, 6 c and 6 d of the wave-front demultiplexer 232 through, e.g., four parallel channels, such as wireless channels or physical channels. The input ports 6 a, 6 b, 6 c and 6 d are arranged in parallel. Next, the wave-front demultiplexer 232 performs the above-mentioned wave-front demultiplexing transformation to process the digital signals S₁, S₂, S₃ and S₄ into multiple linear combinations, each combined with the digital signals S₁, S₂, S₃ and S₄ multiplied by respective weightings, represented by the digital signals Z₁, Z₂, Z₃ and Z₄ output in parallel from the four parallel output ports 7 a, 7 b, 7 c and 7 d of the wave-front demultiplexer 232. The digital signals Z₁, Z₂, Z₃ and Z₄ are digital representations of the analog signals X₁, X₂, X₃ and X₄, respectively. The four output ports 7 a, 7 b, 7 c and 7 d are arranged in parallel.

According to another exemplary embodiment of the present disclosure, three of the four analog signals X₁, X₂, X₃ and X₄ illustrated in FIG. 2A can be replaced with three analog pilot or diagnostic signals. That is, the system 200 illustrated in FIG. 2A can receive one extraneous analog signal X₁ and three analog pilot or diagnostic signals X₂, X₃ and X₄ and sends the four signals X₁, X₂, X₃ and X₄ to the input ports 2 a, 2 b, 2 c and 2 d of the wave-front multiplexer 213. Each of the analog pilot or diagnostic signals X₂, X₃ and X₄ may have a single frequency and fixed amplitude. Next, the signals X₁, X₂, X₃ and X₄ are processed by the wave-front multiplexer 213, the analog-to-digital converters 220 a, 220 b, 220 c and 220 d, and the wave-front demultiplexer 232, as mentioned above. Next, the wave-front demultiplexer 232 outputs a digital representation of the extraneous analog signal X₁, represented by the digital signal Z₁, and outputs digital representations of the analog pilot or diagnostic signals X₂, X₃ and X₄, represented by the digital signals Z₂, Z₃ and Z₄. Alternatively, each of the analog pilot or diagnostic signals X₂, X₃ and X₄ could change based on time or could be any signal known by the system 200. The extraneous analog signal X₁ is unknown by the system 200 and input into the system 200 from an extraneous system.

According to another exemplary embodiment of the present disclosure, one of the four analog signals X₁, X₂, X₃ and X₄ illustrated in FIG. 2A can be replaced with an analog ground signal. For example, three extraneous analog signals X₁, X₂ and X₃ that could be independent to one another and one analog ground signal X₄ are input to the input ports 2 a, 2 b, 2 c and 2 d of the wave-front multiplexer 213 illustrated in FIG. 2A. Next, the signals X₁, X₂, X₃ and X₄ are processed by the wave-front multiplexer 213, the analog-to-digital converters 220 a, 220 b, 220 c and 220 d, and the wave-front demultiplexer 232, as mentioned above. Next, the wave-front demultiplexer 232 outputs three digital representations of the three extraneous analog signals X₁, X₂ and X₃, represented by the three digital signals Z₁, Z₂ and Z₃, and outputs a digital representation of the analog ground signal X₄, represented by the digital signal Z₄.

According to another exemplary embodiment of the present disclosure, the system 200 may further include an equalizer and an optimizer to dynamically adjust digital signals output from analog-to-digital converters before the digital signals are transmitted into the wave-front demultiplexer 232. FIG. 2B shows an example illustrating how the system 200 optimizes, compensates and/or equalizes four digital signals W₁, W₂, W₃ and W₄, output from the analog-to-digital converters 200 a, 200 b, 200 c and 200 d, based on factors including a variation in a pilot or diagnostic signal Z₄ output from the wavefront demultiplexer 232 and the correlations between each two of the digital signals Z₁, Z₂, Z₃ and Z₄.

Referring to FIG. 2B, an analog-to-digital conversion system 200 may include a wave-front multiplexer 213, four individual analog-to-digital converters 220 a, 220 b, 220 c and 220 d, an equalizer or equalization processor 231, a wave-front demultiplexer 232, and an optimizer or optimization processor 235. The system 200 illustrated in FIG. 2B is similar to the system 200 illustrated in FIG. 2A except that the system 200 illustrated in FIG. 2B further includes the equalizer 231 and the optimizer 235 and that the extraneous analog signal X₄ illustrated in FIG. 2A is replaced with an analog pilot or diagnostic signal X₄ shown in FIG. 2B. In this embodiment, the four processing units or devices 999 a, 999 b, 999 c and 999 d as illustrated in FIG. 1B can be replaced with the four analog-to-digital converters 220 a, 220 b, 220 c and 220 d illustrated in FIG. 2B.

A method for processing signals or data streams by using the system 200 shown in FIG. 2B is described below. Three extraneous analog signals X₁, X₂ and X₃ from, e.g., one or more wireless base stations or array elements such as antenna array elements and the pilot or diagnostic signal X₄ are input in parallel to input ports 2 a, 2 b, 2 c and 2 d of the wave-front multiplexer 213 through, e.g., four parallel signal paths, four parallel wireless channels or four parallel physical channels. Each of the wireless base stations can be, but not limited to, a mobile base station or a Wi-Fi base station. Alternatively, the analog signals X₁, X₂ and X₃ can come from, but not limited to, one or more microphone devices, one or more image sensors, one or more MEMS microphone chips, or one or more antennas of a mobile phone.

The extraneous analog signals X₁, X₂ and X₃ could be independent from one another. The pilot or diagnostic signal X₄ may have a single frequency and fixed amplitude. Alternatively, the analog pilot or diagnostic signal X₄ could change based on time or could be any signal known by the system 200. The extraneous analog signals X₁, X₂ and X₃ are unknown by the system 200 and input into the system 200 from an extraneous system.

Next, the wave-front multiplexer 213 performs the above wave-front multiplexing transformation to process the signals X₁, X₂, X₃ and X₄ into multiple linear combinations, each combined with the signals X₁, X₂, X₃ and X₄ multiplied by respective weightings, represented by four analog signals Y₁, Y₂, Y₃ and Y₄. Next, the wave-front multiplexer 213 outputs the analog signals Y₁, Y₂, Y₃ and Y₄ from its output ports 3 a, 3 b, 3 c and 3 d, and the analog signals Y₁, Y₂, Y₃ and Y₄ are respectively transmitted into four input ports 4 a, 4 b, 4 c and 4 d of the four analog-to-digital converters 220 a, 220 b, 220 c and 220 d through, e.g., four parallel channels, such as wireless channels or physical channels.

After the analog signals Y₁, Y₂, Y₃ and Y₄ are transmitted in parallel into the analog-to-digital converters 220 a, 220 b, 220 c and 220 d arranged in parallel, the analog-to-digital converters 220 a, 220 b, 220 c and 220 d convert the analog signals Y₁, Y₂, Y₃ and Y₄ into digital representations of the analog signals Y₁, Y₂, Y₃ and Y₄, respectively represented by the digital signals W₁, W₂, W₃ and W₄, and output the digital signals W₁, W₂, W₃ and W₄ in parallel from output ports 5 a, 5 b, 5 c and 5 d of the analog-to-digital converters 220 a, 220 b, 220 c and 220 d. The analog signals Y₁, Y₂, Y₃ and Y₄ may be sampled at the same sampling frequency or at different sampling frequencies by the analog-to-digital converters 220 a, 220 b, 220 c and 220 d.

Next, the digital signals W₁, W₂, W₃ and W₄ are transmitted in parallel to four input ports 10 a, 10 b, 10 c and 10 d of the equalizer 231 through, e.g., four parallel signal paths, four parallel wireless channels, or four parallel physical channels. The input ports 10 a, 10 b, 10 c and 10 d are arranged in parallel for receiving the digital signals W₁, W₂, W₃ and W₄, respectively. After the digital signals W₁, W₂, W₃ and W₄ are transmitted in parallel into the equalizer 231, an optimizing and equalizing process is performed such that the digital signals W₁, W₂, W₃ and W₄ can be compensated to be multiplied by four respective weightings by the equalizer 231, wherein the four respective weightings of the equalizer 231 can be adjusted based on a control signal CS output from the optimizer 235 and input into the equalizer 231. The optimizing and equalizing process can be referred to as the optimizing and equalizing process as illustrated in FIGS. 1B and 1C. After the optimizing and equalizing process, the equalizer 231 outputs four equalized digital signals S₁, S₂, S₃ and S₄, respectively, from its output ports 11 a, 11 b, 11 c and 11 d. The equalized digital signal S₁ is created by the equalizer 231 multiplying the digital signal W₁ by one of the weightings of the equalizer 231, the equalized digital signal S₂ is created by the equalizer 231 multiplying the digital signal W₂ by another one of the weightings of the equalizer 231, the equalized digital signal S₃ is created by the equalizer 231 multiplying the digital signal W₃ by another one of the weightings of the equalizer 231, and the equalized digital signal S₄ is created by the equalizer 231 multiplying the digital signal W₄ by the other one of the weightings of the equalizer 231. Next, the equalized digital signals S₁, S₂, S₃ and S₄ are transmitted in parallel into input ports 6 a, 6 b, 6 c and 6 d of the wave-front demultiplexer 232 through four parallel signal paths between the output ports 11 a, 11 b, 11 c and 11 d of the equalizer 231 and the input ports 6 a, 6 b, 6 c and 6 d of the wave-front demultiplexer 232. Each of the four respective weightings of the equalizer 231 can be, but not limited to, a complex value such that the equalized signals S₁, S₂, S₃ and S₄ can be rotated precisely to become in phase. In this case, the equalizer 231 can be performed by the narrow band equalizer, as illustrated in FIG. 1C. The narrow band equalizer 231 can provide phase and amplitude modifications to each of the signals W₁, W₂, W₃ and W₄ featuring a constant phase shift and a constant amplitude attenuation across a narrow frequency band. Alternatively, the equalizer 231 can be performed by the broadband equalizer, as illustrated in FIG. 1C. The broadband equalizer 231 can provide phase and amplitude modifications to each of the signals W₁, W₂, W₃ and W₄ featuring a constant phase shift and a constant amplitude attenuation in each sub-band across a broad frequency band, but the phase shift and amplitude attenuation in one sub-band across the broad frequency band is different from those in the other sub-bands across the broad frequency band.

After the equalized digital signals S₁, S₂, S₃ and S₄ are input in parallel to the wave-front demultiplexer 232, the wave-front demultiplexer 232 performs the above wave-front demultiplexing transformation to process the equalized digital signals S₁, S₂, S₃ and S₄ into multiple linear combinations, each combined with the equalized digital signals S₁, S₂, S₃ and S₄ multiplied by respective weightings, represented by the digital signals Z₁, Z₂, Z₃ and Z₄ output in parallel from the four parallel output ports 7 a, 7 b, 7 c and 7 d of the wave-front demultiplexer 232. The digital signals Z₁, Z₂, Z₃ and Z₄ are digital representations of the analog signals X₁, X₂, X₃ and X₄, respectively. The four output ports 7 a, 7 b, 7 c and 7 d are arranged in parallel. Each of the digital signals Z₁, Z₂ and Z₃ can be, but not limited to, a RF digital signal or an IF digital signal.

The optimizer 235 can be in a signal path between the output ports 7 a, 7 b, 7 c and 7 d and the equalizer 231 (only one signal path between the output port 7 d and the equalizer 231 is shown in FIG. 2B). The flow chart of the optimizing and equalizing process shown in FIG. 1C can be applied to the embodiment illustrated in FIG. 2B.

The equalizer 231, the wave-front demultiplexer 232 and the optimizer 235 can be, but not limited to, embedded in a processor 230, such as single integrated circuit chip or single chip package. The equalizer 231 can be hardware or can be realized by software installed in and performed by the processor 230. The optimizer 235 can be hardware or can be realized by software installed in and performed by the processor 230.

Alternatively, the system 200 can process more than four input signals, such as seven analog signals X₁-X₇ and one analog pilot or diagnostic signal X₈ as illustrated in FIG. 2C, and can output more than four output signals, such as seven digital signals Z₁-Z₇ and one digital pilot or diagnostic signal Z₈ as illustrated in FIG. 2C. Moreover, the system 200 can include more than four A/D converters, such as eight A/D converters 220 a-220 h illustrated in FIG. 2C, in more than four parallel signal paths or channels between the wave-front multiplexer 213 and the equalizer 231 and can further include more than four processing units, such as eight frequency down-conversion components 216 a-216 h illustrated in FIG. 2C, in more than four parallel signal paths or channels between more than four output ports of the wave-front multiplexer 213 and more than four input ports of the A/D converters, such as in eight parallel signal paths or channels between eight outputs 3 a-3 h of the wave-front multiplexer 213 and eight inputs 4 a-4 h of the A/D converters 220 a-220 h. All of the processing units (such as the components 216 a-216 h illustrated in FIG. 2C) and the wave-front multiplexer 213 can be, but not limited to, embedded in a processor 210, such as integrated circuit chip, system-on chip or chip package. Alternatively, the wave-front multiplexer 213 may be embedded in the processor 210, but the processing units (such as the components 216 a-216 h illustrated in FIG. 2C) may be embedded in another processor, such as integrated circuit chip, system-on chip or chip package, or in multiple processors, such as integrated circuit chips, system-on chips or chip packages, respectively.

A method for processing signals or data streams by using the system 200 shown in FIG. 2C is described below. Referring to FIG. 2C, the seven analog signals X₁-X₇ from, e.g., one or more wireless base stations or array elements such as antenna array elements and the analog pilot or diagnostic signal X₈ are input in parallel to eight input ports 2 a-2 h of the wave-front multiplexer 213 through, e.g., eight parallel signal paths, eight parallel wireless channels, or eight parallel physical channels. The seven analog signals X₁-X₇ could be, but not limited to, seven independent RF signals. Each of the wireless base stations can be, but not limited to, a mobile base station or a Wi-Fi base station. Alternatively, the analog signals X₁-X₇ can come from, but not limited to, one or more microphone devices, one or more image sensors, one or more MEMS microphone chips, or one or more antennas of a mobile phone.

The pilot or diagnostic signal X₈ may have a single frequency and fixed amplitude. Alternatively, the pilot or diagnostic signal X₈ could change based on time or could be any signal known by the system 200. In contrast, the extraneous signals X₁-X₇ are unknown by the system 200 and input into the system 200 from an extraneous system.

Next, referring to FIG. 2C, the wave-front multiplexer 213 performs the above-mentioned wave-front multiplexing transformation to process the eight signals X₁-X₈ into eight linear combinations, each combined with the signals X₁-X₈ multiplied by respective weightings, represented by eight analog signals Y₁-Y₈, which can be referred to as the description illustrated in FIG. 1D. In this case, the number of H is equal to 8. The wave-front multiplexer 213 may include 8*8 computing units and eight summing processors. The computing units form a processor array with eight rows and eight columns. The input signals X₁-X₈ can be received by the computing units in the respective eight columns in the processor array. Upon receiving the input signals X₁-X₈, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The eight summing processors can output the eight signals Y₁-Y₈ each combined with the weighted signals output from the computing units in a corresponding one of the eight rows in the processor array. An 8×8 Butler matrix may be used as the wave-front multiplexer 213 illustrated in FIG. 2C.

Next, referring to FIG. 2C, the wave-front multiplexer 213 outputs the eight analog signals Y₁-Y₈ from its eight output ports 3 a-3 h arranged in parallel, and the eight analog signals Y₁-Y₈ are respectively transmitted to eight input ports 8 a-8 h of the eight frequency down-conversion components 216 a-216 h through, e.g., eight parallel signal paths, eight parallel wireless channels, or eight parallel physical channels. After the eight signals Y₁-Y₈ are respectively input into the eight frequency down-conversion components 216 a-216 h, the eight signals Y₁-Y₈ have frequency ranges down-converted into lower ones by the frequency down-conversion components 216 a-216 h, and the eight frequency down-conversion components 216 a-216 h output the eight frequency down-converted signals, represented by eight signals G₁-G₈, form their output ports 9 a-9 h, respectively. For example, the eight signals Y₁-Y₈ can be, but not limited to, eight Ka-band or Ku-band analog signals, and the eight frequency down-conversion components 216 a-216 h can respectively convert the eight Ka-band or Ku-band analog signals Y₁-Y₈ into eight intermediate-frequency (IF) or base-band analog signals G₁-G₈.

Next, referring to FIG. 2C, the eight signals G₁-G₈ are respectively transmitted to eight input ports 4 a-4 h of the eight A/D converters 220 a-220 h through, e.g., eight parallel signal paths, eight parallel wireless channels or eight parallel physical channels, and the eight A/D converters 220 a-220 h respectively convert the eight analog signals G₁-G₈ into their digital representations, represented by eight digital signals W₁-W₈, and respectively output the eight digital signals W₁-W₈ from their output ports 5 a-5 h. The eight analog signals G₁-G₈ may be sampled at the same sampling frequency or at different sampling frequencies by the eight A/D converters 220 a-220 h.

Next, referring to FIG. 2C, the eight digital signals W₁-W₈ are transmitted in parallel to eight input ports 10 a-10 h of the equalizer 231 through, e.g., eight parallel signal paths, eight parallel wireless channels or eight parallel physical channels. The eight input ports 10 a-10 h are arranged in parallel for receiving the eight digital signals W₁-W₈, respectively. After the digital signals W₁-W₈ are transmitted in parallel into the equalizer 231, an optimizing and equalizing process is performed such that each of the digital signals W₁-W₈ can be compensated to be multiplied by one of eight respective weightings by the equalizer 231, wherein the eight respective weightings of the equalizer 231 can be adjusted based on a control signal CS, output from the optimizer 235 and input into the equalizer 231. The optimizing and equalizing process can be referred to as the optimizing and equalizing process as illustrated in FIG. 1C.

Referring to FIG. 2C, after the optimizing and equalizing process, the equalizer 231 outputs eight equalized digital signals S₁-S₈, respectively, from its eight output ports 11 a-11 h. The equalized digital signal S₁ is created by the equalizer 231 multiplying the digital signal W₁ by one of the weightings of the equalizer 231. The equalized digital signal S₂ is created by the equalizer 231 multiplying the digital signal W₂ by another one of the weightings of the equalizer 231. The equalized digital signal S₃ is created by the equalizer 231 multiplying the digital signal W₃ by another one of the weightings of the equalizer 231. The equalized digital signal S₄ is created by the equalizer 231 multiplying the digital signal W₄ by another one of the weightings of the equalizer 231. The equalized digital signal S₅ is created by the equalizer 231 multiplying the digital signal W₅ by another one of the weightings of the equalizer 231. The equalized digital signal S₆ is created by the equalizer 231 multiplying the digital signal W₆ by another one of the weightings of the equalizer 231. The equalized digital signal S₇ is created by the equalizer 231 multiplying the digital signal W₇ by another one of the weightings of the equalizer 231. The equalized digital signal S₈ is created by the equalizer 231 multiplying the digital signal W₈ by the other one of the weightings of the equalizer 231. Each of the four respective weightings of the equalizer 231 can be, but not limited to, a complex value such that the equalized signals S₁-S₈ can be rotated precisely to become in phase. In this case, the equalizer 231 can be performed by the narrow band equalizer, as illustrated in FIG. 1C. The narrow band equalizer 231 can provide phase and amplitude modifications to each of the signals W₁-W₈ featuring a constant phase shift and a constant amplitude attenuation across a narrow frequency band. Alternatively, the equalizer 231 can be performed by the broadband equalizer, as illustrated in FIG. 1C. The broadband equalizer 231 can provide phase and amplitude modifications to each of the signals W₁-W₈ featuring a constant phase shift and a constant amplitude attenuation in each sub-band across a broad frequency band, but the phase shift and amplitude attenuation in one sub-band across the broad frequency band is different from those in the other sub-bands across the broad frequency band.

Next, referring to FIG. 2C, the equalized digital signals S₁-S₈ are transmitted in parallel into eight input ports 6 a-6 h of the wave-front demultiplexer 232 through eight parallel signal paths between the output ports 11 a-11 h of the equalizer 231 and the input ports 6 a-6 h of the wave-front demultiplexer 232.

Referring to FIG. 2C, after the eight equalized digital signals S₁-S₈ are input in parallel to the wave-front demultiplexer 232, the wave-front demultiplexer 232 performs the above-mentioned wave-front demultiplexing transformation to process the eight equalized digital signals S₁-S₈ into eight linear combinations, each combined with the equalized digital signals S₁-S₈ multiplied by respective weightings, represented by the eight digital signals Z₁-Z₈ output in parallel from its eight parallel output ports 7 a-7 h, which can be referred to as the description illustrated in FIG. 1E. In this case, the number of I is equal to 8. The wave-front demultiplexer 232 may include 8*8 computing units and eight summing processors. The computing units form a processor array with eight rows and eight columns. The input signals S₁-S₈ can be received by the computing units in the respective eight columns in the processor array. Upon receiving the input signals S₁-S₈, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The eight summing processors can output the eight signals Z₁-Z₈ each combined with the weighted signals output from the computing units in a corresponding one of the eight rows in the processor array.

Referring to FIG. 2C, the eight digital signals Z₁-Z₈ are eight digital representations of the eight analog signals X₁-X₈, respectively. The eight output ports 7 a-7 h are arranged in parallel. Each of the seven digital signals Z₁-Z₇ can be, but not limited to, a RF digital signal or an IF digital signal.

Referring to FIG. 2C, the optimizer 235 can be in a signal path between the output ports 7 a-7 h and the equalizer 231. Only one signal path between the output port 7 h and the equalizer 231 is shown in FIG. 2C. The optimizer 235 can output the control signal CS to the equalizer 231 so as to adjust the eight respective weightings of the equalizer 231 when the optimizing and equalizing process, as illustrated in FIG. 1C, is performed. In FIG. 2C, the equalizer 231, the wave-front demultiplexer 232 and the optimizer 235 can be, but not limited to, embedded in a processor 230, such as single integrated circuit chip or single chip package.

Alternatively, the analog-to-digital conversion system 200 can include an M-to-1 time-division multiplexer with M input ports receiving M parallel input signals and one output port outputting an output signal, where M is an integer. The integer M can be, but not equal to, equal to the total number of input ports of the wave-front multiplexer 213, equal to the total number of output ports of the wave-front multiplexer 213, equal to the total number of input ports of the wave-front demultiplexer 232, equal to the total number of output ports of the wave-front demultiplexer 232, equal to the total number of A/D converters of the system 200, equal to the total number of frequency down-conversion components of the system 200, equal to the total number of signals input into the wave-front multiplexer 213, and/or equal to the total number of signals output from the wave-front demultiplexer 232. The M-to-1 time-division multiplexer is defined herein to arrange or align the number M of parallel input signals sequentially in time as an output signal output from the output port of the M-to-1 time-division multiplexer. The output signal at the output port of the M-to-1 time-division multiplexer features M times the sampling rate as each of signals at output ports of the A/D converters features. The output signal at the output port of the M-to-1 time-division multiplexer features the same dynamic range as each of signals at output ports of the A/D converters features. In this case, one of the input ports of the wave-front multiplexer 213 receives an extraneous analog signal, and the others receive ground signals, wherein one or more of the ground signals can be used as pilot or diagnostic signals, or are connected to a ground reference.

The M-to-1 time-division multiplexer, for example, can be applied to the system 200 illustrated in FIG. 2C. That is, the system 200 illustrated in FIG. 2C further includes the M-to-1 time-division multiplexer. In this case, the M-to-1 time-division multiplexer is an 8-to-1 time-division multiplexer with eight input ports receiving the eight equalized digital signals S₁-S₈ illustrated in FIG. 2C and an output port outputting an output signal arranged or aligned as the eight equalized digital signals S₁-S₈ sequentially in time. Moreover, the input port 2 a of the wave-front multiplexer 213 illustrated in FIG. 2C receives an extraneous analog signal X₁ from, e.g., a wireless base station, an antenna array, a microphone device, an image sensor, a MEMS microphone chip or an antenna of a mobile phone, and the other input ports 2 b-2 h of the wave-front multiplexer 213 illustrated in FIG. 2C receive seven ground signals X₂-X₈ or are connected to a ground reference. The ground signal X₈ is used as a pilot or diagnostic signal. Thereby, the output signal at the output port of the 8-to-1 time-division multiplexer features eight times the sampling rate as each of the eight signals W₁-W₈ at the eight output ports 5 a-5 h of the eight A/D converters 220 a-220 h features. The output signal at the output port of the 8-to-1 time-division multiplexer features the same dynamic range as each of the eight signals W₁-W₈ at the eight output ports 5 a-5 h of the eight A/D converters 220 a-220 h features.

Alternatively, the M-to-1 time-division multiplexer can be applied to an analog-to-digital conversion system 200 illustrated in FIG. 2D. In this case, the M-to-1 time-division multiplexer is a 4-to-1 time-division multiplexer 55, illustrated in FIG. 2D, with four input ports 12 a-12 d receiving four equalized digital signals S₁-S₄ and an output port 13 outputting an output signal Z₀ arranged or aligned as the four equalized digital signals S₁-S₄ sequentially in time.

Referring to FIG. 2D, the system 200 may include a wave-front multiplexer 213, four frequency down-conversion components 216 a-216 d, four individual A/D converters 220 a-220 d, an equalizer 231, a wave-front demultiplexer 232, an optimizer 235, and the 4-to-1 time-division multiplexer 55. The description of the wave-front multiplexer 213 illustrated in FIG. 2D can be referred to as the description of the wave-front multiplexer 213 as illustrated in FIG. 1B or 2B. The description of the wave-front demultiplexer 232 illustrated in FIG. 2D can be referred to as the description of the wave-front demultiplexer 232 as illustrated in FIG. 1B or 2B. The description of the equalizer 231 illustrated in FIG. 2D can be referred to as the description of the equalizer 231 as illustrated in FIG. 1B or 2B. The description of the optimizer 235 illustrated in FIG. 2D can be referred to as the description of the optimizer 235 as illustrated in FIG. 1B or 2B.

Referring to FIG. 2D, the wave-front multiplexer 213 and the four frequency down-conversion components 216 a-216 d can be, but not limited to, embedded in a processor 210, such as integrated circuit chip, system-on chip or chip package. Alternatively, the wave-front multiplexer 213 may be embedded in the processor 210, but the four frequency down-conversion components 216 a-216 d may be embedded in another processor, such as integrated circuit chip, system-on chip or chip package, or in four processors, such as four integrated circuit chips, four system-on chips or four chip packages, respectively. The wave-front multiplexer 213 can be, but not limited to, realized by hardware such as 4×4 Butler matrix, and each of the frequency down-conversion components 216 a-216 d can be, but not limited to, realized by hardware. The equalizer 231, the wave-front demultiplexer 232, the optimizer 235, and the 4-to-1 time-division multiplexer 55 can be, but not limited to, embedded in a processor 230, such as integrated circuit chip, system-on chip or chip package. Alternatively, the equalizer 231, the wave-front demultiplexer 232 and the optimizer 235 may be embedded in the processor 210, but the 4-to-1 time-division multiplexer 55 may be embedded in another processor, such as integrated circuit chip, system-on chip or chip package.

A method for processing one or more data streams or signals by using the system 200 shown in FIG. 2D is described below. Referring to FIG. 2D, an extraneous analog signal X₁ from, e.g., a wireless base station or an antenna array and three ground signals X₂, X₃ and X₄ are input in parallel to four input ports 2 a-2 d of the wave-front multiplexer 213 through, e.g., four parallel signal paths, four parallel wireless channels or four parallel physical channels. The wireless base station can be, but not limited to, a mobile base station or a Wi-Fi base station. Alternatively, the analog signal X₁ can come from, but not limited to, a microphone device, an image sensor, a MEMS microphone chip, or an antenna of a mobile phone. The ground signal X₄ is used as an input pilot or diagnostic signal. Alternatively, two or all of the three ground signals X₂, X₃ and X₄ can be used as input pilot or diagnostic signals.

Referring to FIG. 2D, after the four signals X₁, X₂, X₃ and X₄ are input into the wave-front multiplexer 213, the wave-front multiplexer 213 performs the above-mentioned wave-front multiplexing transformation to process the four signals X₁-X₄ into four linear combinations, each combined with the signals X₁-X₄ multiplied by respective weightings, represented by four analog signals Y₁-Y₄, which can be referred to as the description illustrated in FIG. 1D. In this case, the number of H is equal to 4. The wave-front multiplexer 213 may include 4*4 computing units and four summing processors. The computing units form a processor array with four rows and four columns. The input signals X₁-X₄ can be received by the computing units in the respective four columns in the processor array. Upon receiving the input signals X₁-X₄, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The four summing processors can output four analog signals Y₁-Y₄ each combined with the weighted signals output from the computing units in a corresponding one of the four rows in the processor array.

Next, referring to FIG. 2D, the wave-front multiplexer 213 outputs the four analog signals Y₁-Y₄ from its four output ports 3 a-3 d arranged in parallel, and the four analog signals Y₁-Y₄ are respectively transmitted to four input ports 8 a-8 d of the four frequency down-conversion components 216 a-216 d through, e.g., four parallel signal paths, four parallel wireless channels or four parallel physical channels. After the four analog signals Y₁-Y₄ are input into the four frequency down-conversion components 216 a-216 d, the four analog signals Y₁-Y₄ have frequency ranges down-converted into lower ones by the frequency down-conversion components 216 a-216 d, and the four frequency down-conversion components 216 a-216 d output the four frequency down-converted signals, represented by four signals G₁-G₄, from their output ports 9 a-9 d, respectively. For example, the four analog signals Y₁-Y₄ can be, but not limited to, four Ka-band or Ku-band analog signals, and the four frequency down-conversion components 216 a-216 d can respectively convert the four Ka-band or Ku-band analog signals Y₁-Y₄ into four intermediate-frequency (IF) or baseband analog signals G₁-G₄.

Next, referring to FIG. 2D, the four signals G₁-G₄ are respectively transmitted to four input ports 4 a-4 d of the four A/D converters 220 a-220 d, and the four A/D converters 220 a-220 d respectively convert the four analog signals G₁-G₄ into their digital representations, represented by four digital signals W₁-W₄, and respectively output the four digital signals W₁-W₄ from their output ports 5 a-5 d. The four analog signals G₁-G₄ may be sampled at the same sampling frequency or at different sampling frequencies by the four A/D converters 220 a-220 d.

Next, referring to FIG. 2D, the four digital signals W₁-W₄ are transmitted in parallel to four input ports 10 a-10 d of the equalizer 231 through, e.g., four parallel signal paths, four parallel wireless channels or four parallel physical channels. The four input ports 10 a-10 d are arranged in parallel for receiving the four digital signals W₁-W₄, respectively. After the four digital signals W₁-W₄ are transmitted in parallel into the equalizer 231, an optimizing and equalizing process as illustrated in FIGS. 1B and 1C can be applied herein to compensating each of the four digital signals W₁-W₄ to be multiplied by a weighting of the equalizer 231, wherein the weighting of the equalizer 231 can be adjusted based on a control signal CS output from the optimizer 235 and input into the equalizer 231.

Referring to FIG. 2D, after the optimizing and equalizing process, the equalizer 231 outputs four equalized digital signals S₁-S₄, respectively, from its four output ports 11 a-11 d to four input ports 12 a-12 d of the 4-to-1 time-division multiplexer 55 and to four input ports 6 a-6 d of the wave-front demultiplexer 232. The equalized digital signal S₁ is created by the equalizer 231 multiplying the digital signal W₁ by a weighting of the equalizer 231. The equalized digital signal S₂ is created by the equalizer 231 multiplying the digital signal W₂ by another weighting of the equalizer 231. The equalized digital signal S₃ is created by the equalizer 231 multiplying the digital signal W₃ by another weighting of the equalizer 231. The equalized digital signal S₄ is created by the equalizer 231 multiplying the digital signal W₄ by the other weighting of the equalizer 231. Each of the weightings of the equalizer 231 can be, but not limited to, a complex value such that the equalized signals S₁-S₄ can be rotated precisely to become in phase. In this case, the equalizer 231 can be performed by the narrow band equalizer, as illustrated in FIG. 1C. Alternatively, the equalizer 231 can be performed by the broadband equalizer, as illustrated in FIG. 1C.

Referring to FIG. 2D, after the four equalized digital signals S₁-S₄ are input in parallel to the 4-to-1 time-division multiplexer 55, the 4-to-1 time-division multiplexer 55 arranges or aligns the four equalized digital signals S₁-S₄ sequentially in time as an output digital signal Z₀ output from its output port 13. With the multiplexing performed by the 4-to-1 time-division multiplexer 55, the four equalized digital signals S₁-S₄ output from the equalizer 231 are not coherently combined but are arranged sequentially in time as the output digital signal Z₀. The digital signal Z₀ is a digital representation of the analog signal X₁ and can be, but not limited to, a RF digital signal or an IF digital signal.

Referring to FIG. 2D, the output digital signal Z₀ at the output port 13 of the 4-to-1 time-division multiplexer 55 features four times the sampling rate as each of the four digital signals W₁-W₄ at the four output ports 5 a-5 d of the four A/D converters 220 a-220 d features. The output digital signal Z₀ at the output port 13 of the 4-to-1 time-division multiplexer 55 features the same dynamic range as each of the four digital signals W₁-W₄ at the four output ports 5 a-5 d of the four A/D converters 220 a-220 d features.

Referring to FIG. 2D, after the four equalized digital signals S₁-S₄ are input in parallel to the wave-front demultiplexer 232, the wave-front demultiplexer 232 performs the above-mentioned wave-front demultiplexing transformation to process the four equalized digital signals S₁-S₄ into four linear combinations, each combined with the equalized digital signals S₁-S₄ multiplied by respective weightings, represented by four digital signals Z₁-Z₄ output in parallel from its four parallel output ports 7 a-7 d, which can be referred to as the description illustrated in FIG. 1E. In this case, the number of I is equal to 4. The wave-front demultiplexer 232 may include 4*4 computing units and four summing processors. The computing units form a processor array with four rows and four columns. The input signals S₁-S₄ can be received by the computing units in the respective four columns in the processor array. Upon receiving the input signals S₁-S₄, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The four summing processors can output the four signals Z₁-Z₄ each combined with the weighted signals output from the computing units in a corresponding one of the four rows in the processor array. The digital signal Z₁ is a digital representation of the analog signal X₁, and the three digital ground signals Z₂-Z₄ are three digital representations of the three ground signals X₂-X₄.

Referring to FIG. 2D, due to coherent combining of the wave-front demultiplexer 232, the digital signal Z₁ at the output port 7 a of the wave-front demultiplexer 232 features the same sampling rate as each of the four digital signals W₁-W₄ at the four output ports 5 a-5 d of the four A/D converters 220 a-220 d features. The digital signal Z₁ at the output port 7 a of the wave-front demultiplexer 232 features a dynamic range better than each of the four digital signals W₁-W₄ at the four output ports 5 a-5 d of the four A/D converters 220 a-220 d features and better than the output digital signal Z₀ at the output port 13 of the 4-to-1 time-division multiplexer 55 features. The output digital signal Z₀ at the output port 13 of the 4-to-1 time-division multiplexer 55 features four times the sampling rate as the digital signal Z₁ at the output port 7 a of the wave-front demultiplexer 232 features.

Referring to FIG. 2D, the digital signal Z₁ can be, but not limited to, a RF digital signal or an IF digital signal. The signal Z₄ can be used as an output pilot or diagnostic signal featuring a value to be compared with that featured by the input pilot or diagnostic signal X₄ during the optimizing and equalizing process. The optimizer 235 can receive one or more of the signals Z₁-Z₄ (i.e. only the signal Z₄ is shown in FIG. 2D) output from the wave-front demultiplexer 232 and outputs the control signal CS to the equalizer 231 so as to adjust the four respective weightings of the equalizer 231 when the optimizing and equalizing process is performed.

Alternatively, the equalizer 231, the wave-front demultiplexer 232 and the optimizer 235 of the system 200 illustrated in FIG. 2D can be omitted, that is, the processor 230 illustrated in FIG. 2D may not include the equalizer 231, the wave-front demultiplexer 232 and the optimizer 235. In this case, the four digital signals W₁-W₄ output from the four A/D converters 220 a-220 d are transmitted to the 4-to-1 time-division multiplexer 55, and the 4-to-1 time-division multiplexer 55 arranges or aligns the four digital signals W₁-W₄ sequentially in time as an output digital signal Z₀ output from its output port 13. With the multiplexing performed by the 4-to-1 time-division multiplexer 55, the four digital signals W₁-W₄ output from the four A/D converters 220 a-220 d are not coherently combined but are arranged sequentially in time as the output digital signal Z₀. The digital signal Z₀ is a digital representation of the analog signal X₁ and can be, but not limited to, a RF digital signal or an IF digital signal. The output digital signal Z₀ at the output port 13 of the 4-to-1 time-division multiplexer 55 features four times the sampling rate as each of the four digital signals W₁-W₄ at the four output ports 5 a-5 d of the four A/D converters 220 a-220 d features. The output digital signal Z₀ at the output port 13 of the 4-to-1 time-division multiplexer 55 features the same dynamic range as each of the four digital signals W₁-W₄ at the four output ports 5 a-5 d of the four A/D converters 220 a-220 d features.

Alternatively, the signal X₄, input to the input port 2 d of the wave-front multiplexer 213 illustrated in FIG. 2D, cannot be a ground signal but can be used as a pilot or diagnostic signal. In this case, the signal X₄, input to the input port 2 d of the wave-front multiplexer 213 illustrated in FIG. 2D, may have a single frequency and fixed amplitude. Alternatively, the signal X₄, input to the input port 2 d of the wave-front multiplexer 213 illustrated in FIG. 2D, could change based on time or could be any signal known by the system 200. In contrast, the extraneous signals X₁, input to the input port 2 a of the wave-front multiplexer 213 illustrated in FIG. 2D, is unknown by the system 200 and input into the system 200 from an extraneous system. Moreover, in this case, the wave-front demultiplexer 232 can output a digital representation of the analog signal X₁ from its output port 7 a.

Second Embodiment: Application to Digital Beam Forming Network (DBFN)

FIG. 3A shows a system for performing a broadband (BB) DBFN via four narrowband (NB) DBFN modules grouped with sixteen wave-front multiplexers and four wave-front demultiplexers according to an exemplary embodiment of the present disclosure. In FIG. 3A, the signals with the same reference number may not represent the signals carrying the same information.

Referring to FIG. 3A, a system 700 may include sixteen preprocessor modules 800 a-800 p having the same architecture as one another, four narrowband DBFN modules 801 a-801 d having the same architecture as one another, and four post-processor modules 802 a-802 d having the same architecture as one another. Each of the narrowband DBFN modules 801 a-801 d can perform one or more weighting summations to signals input into said each of the narrowband DBFN modules 801 a-801 d and outputs one or more linear combinations, each combined with the input signals multiplied by respective weightings, which can be realized by hardware, such as field programmable gate arrays (FPGA), fixed-function off-the-shelf digital components, and digital signal processors, or software installed in the system 700.

Referring to FIG. 3A, for brief description, only one of the sixteen preprocessor modules 800 a-800 p is illustrated as below. The preprocessor module 800 a having the same architecture as each of the fifteen preprocessor modules 800 b-800 p may include a 1-to-3 time-domain demultiplexer (TDDM) 50 and a wave-front multiplexer 213. A time-domain demultiplexer is defined herein to divide an input signal having a high bandwidth sampled at a high sampling rate into multiple output signals each having a low bandwidth sampled at a low sampling rate. For example, in this embodiment, the 1-to-3 time-domain demultiplexer 50 can divide an input digital signal A₀ having a frequency bandwidth of J sampled at a sampling rate of K into three output digital signals X₁, X₂ and X₃, each having a frequency bandwidth of J/3 sampled at a sampling rate of K/3, passing through three parallel signal paths, such as physical or wireless channels, coupled to the wave-front multiplexer 213. A wave-front multiplexer is defined to perform the above wave-front multiplexing transform to process multiple input signals into multiple linear combinations, each combined with the input signals multiplied by respective weightings, which can be referred to as the description illustrated in FIGS. 1A and 1D. In this case, the number of H is equal to 4. The wavefront multiplexer 213 may include 4*4 computing units and four summing processors. The computing units form a processor array with four rows and four columns. The three input signals X₁-X₃ and an input diagnostic or pilot signal X₄ can be received by the computing units in the respective four columns in the processor array. Upon receiving the input signals X₁-X₄, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The four summing processors can output four signals Y₁-Y₄ each combined with the weighted signals output from the computing units in a corresponding one of the four rows in the processor array. For example, in this embodiment, the wave-front multiplexer 213 can receive the digital signals X₁, X₂ and X₃ output from the 1-to-3 time-domain demultiplexer 50 and the digital diagnostic or pilot signal X₄, performing the above wave-front multiplexing transformation to process the input signals X₁, X₂, X₃ and X₄ into four linear combinations, each combined with the signals X₁, X₂, X₃ and X₄ multiplied by respective weightings, represented by the signals Y₁, Y₂, Y₃ and Y₄.

Referring to FIG. 3A, for brief description, only one of the four post-processor modules 802 a-802 d is illustrated as below. The post-processor module 802 a having the same architecture as each of the three post-processor modules 802 b, 802 c and 802 d may include a 3-to-1 time-domain multiplexer (TDM) 51, an equalizer 231, a wave-front demultiplexer 232, and an optimizer 235. A time-domain multiplexer is defined herein to combine or integrate multiple input signals each having a low bandwidth sampled at a low sampling rate into an output signal having a high bandwidth sampled at a high sampling rate. For example, in this embodiment, the 3-to-1 time-domain multiplexer 51 can combine or integrate multiple input signals Z₁, Z₂ and Z₃, each having a frequency bandwidth of J/3 sampled at a sampling rate of K/3, passing through three parallel signal paths, such as physical or wireless channels, coupled to the wave-front demultiplexer 232 into an output signal B₀ having a frequency bandwidth of J sampled at a sampling rate of K. An equalizer is defined to multiply each input signal by a weighting to compensate an amplitude, phase, and time-delay of said each input signal. For example, in this embodiment, the equalizer 231 illustrated in FIGS. 1B and 1C can be applied herein to adjusting amplitudes, phases, and/or time-delays of four signals W₁, W₂, W₃ and W₄ output in parallel from the four DBFN modules 801 a, 801 b, 801 c and 801 d according to a control signal CS generated by the optimizer 235 and generating four equalized signals S₁, S₂, S₃ and S₄ transmitted in parallel to the wave-front demultiplexer 232. The equalized digital signal S₁ is created by the equalizer 231 multiplying the digital signal W₁ by a weighting of the equalizer 231. The equalized digital signal S₂ is created by the equalizer 231 multiplying the digital signal W₂ by another weighting of the equalizer 231. The equalized digital signal S₃ is created by the equalizer 231 multiplying the digital signal W₃ by another weighting of the equalizer 231. The equalized digital signal S₄ is created by the equalizer 231 multiplying the digital signal W₄ by the other weighting of the equalizer 231. A wave-front demultiplexer is defined to perform the above wave-front demultiplexing transform to process multiple input signals into multiple linear combinations, each combined with the input signals multiplied by respective weightings. For example, in this embodiment, the wave-front demultiplexer 232 can receive the four equalized signals S₁, S₂, S₃ and S₄, performing the above wave-front multiplexing transform to process the four input signals S₁, S₂, S₃ and S₄ into four linear combinations, each combined with the signals S₁, S₂, S₃ and S₄ multiplied by respective weightings, represented by four signals Z₁, Z₂, Z₃ and Z₄, which can be referred to as the description illustrated in FIGS. 1A and 1E. In this case, the number of I is equal to 4. The wavefront demultiplexer 232 may include 4*4 computing units and four summing processors. The computing units form a processor array with four rows and four columns. The four input signals S₁-S₄ can be received by the computing units in the respective four columns in the processor array. Upon receiving the four input signals S₁-S₄, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The four summing processors can output the four signals Z₁-Z₄ each combined with the weighted signals output from the computing units in a corresponding one of the four rows in the processor array.

For example, the wave-front multiplexer 213 illustrated in FIG. 3A can perform the wave-front multiplexing transform by using fast Fourier transform, and each wave-front demultiplexer 232 illustrated in FIG. 3A can perform the wave-front demultiplexing transform by using inverse fast Fourier transform to invert or transform signals previously transformed by the wave-front multiplexing transform performed by its complementary wave-front multiplexer 213. Thereby, each of the wave-front multiplexers 213 illustrated in FIG. 3A can be a FFT processor such as a FFT chip, and each of the wave-front demultiplexers 232 illustrated in FIG. 3A can be an IFFT processor such as an IFFT chip.

Besides using the fast Fourier transform, each of the wave-front multiplexers 213 illustrated in FIG. 3A can perform the wave-front multiplexing transform by using any Fourier-related transform, such as discrete Fourier transform, Hartley transform or Hadamard transform, to achieve an orthogonal functional transformation. Besides using the inverse fast Fourier transform, each of the wave-front demultiplexers 232 illustrated in FIG. 3A can perform the wave-front demultiplexing transform by using any inverse Fourier-related transform that can invert or transform signals previously transformed by the wave-front multiplexing transform performed by its complementary wave-front multiplexers 213. Referring to FIG. 3A, each of the DBFN modules 801 a-801 d may include a field programmable gate array (FPGA), a fixed-function off-the-shelf digital component and/or a digital signal processor (DSP) to process a set of signals received from the sixteen wave-front multiplexers 213 of the sixteen preprocessor modules 800 a-800 p. For brief description, only one of the DBFN modules 801 a-801 d is illustrated as below. A DBFN module is defined to output one or more linear combinations, each combined with its input signals multiplied by respective weightings. The DBFN module may include multiple computing units and one or more summing processors, wherein each computing unit independently weights an input signal to generate a weighted signal. Each of the summing processors provides a means for summing all or part of the weighted signals generated by the computing units. For example, referring to FIG. 3B showing a scheme of the DBFN module 801 a, having the same architecture as each of the three DBFN modules 801 b-801 d, in accordance with the present invention, the DBFN module 801 a may include sixty-four computing units (CUs) and four summing processors (SPs). The sixty-four computing units form a 4-by-16 processor array with sixteen columns and four rows, and each of the four summing processors processes the outputs of the corresponding computing units in the same row. The 4-by-16 processor array at each column has four of the sixty-four computing units, and the 4-by-16 processor array at each row has sixteen of the sixty-four computing units. FIG. 3B only shows twelve computing units at the first and second left and first right columns in the process array. The sixty-four computing units receive the sixteen input signals Y₁ output from the sixteen preprocessor modules 800 a-800 p. The preprocessor modules 800 c-800 o are not shown in FIG. 3B. The total number of the input signals Y₁ is sixteen equal to the total number of the preprocessor modules 800 a-800 p.

Referring to FIG. 3B, the four computing units in each column in the processor array receive a corresponding digital signal Y₁ output from a corresponding one of the sixteen preprocessor modules 800 a-800 p, and thus the sixteen digital signals Y₁ output from the sixteen preprocessor modules 800 a-800 p can be received by the sixty-four computing units in the respective sixteen columns in the processor array. Upon receiving the sixteen digital signals Y₁ output from the sixteen preprocessor modules 800 a-800 p, each of the sixty-four computing units independently weights its received digital signal Y₁ to generate a weighted signal. Each of the four summing processors provides a means for summing weighted signals generated by the corresponding sixteen computing units in same row in the processor array to produce a corresponding digital signal or beam W₁, i.e. beam weighting vector, output to the corresponding one of the four post-processor modules 802 a-802 d. Accordingly, the four summing processors can output the four digital signals or beams W₁, each combined with the weighted signals output from the computing units in a corresponding one of the four rows in the processor array. Thereby, the DBFN module 801 a outputs four linear combinations, each combined with the sixteen input signals Y₁ multiplied by respective weightings, represented by the four digital signals W₁, wherein the total number of the linear combinations represented by the signals W₁ is four equal to the total number of the post-processor modules 802 a-802 d.

Referring to FIG. 3B, the DBFN module 801 a can employ digital numerical techniques to create four beam weighting vectors that are four linear combinations, each combined with the sixteen input signals Y₁ in the same corresponding row in its 4-by-16 processor array multiplied by respective weightings, represented by the four signals or beams W₁. The DBFN module 801 b can employ digital numerical techniques to create four beam weighting vectors that are four linear combinations, each combined with the sixteen input signals Y₂ in the same corresponding row in its 4-by-16 processor array multiplied by respective weightings, represented by the four signals or beams W₂. The DBFN module 801 c can employ digital numerical techniques to create four beam weighting vectors that are four linear combinations, each combined with the sixteen input signals Y₃ in the same corresponding row in its 4-by-16 processor array multiplied by respective weightings, represented by the four signals or beams W₃. The DBFN module 801 d can employ digital numerical techniques to create four beam weighting vectors that are four linear combinations, each combined with the sixteen input signals Y₄ in the same corresponding row in its 4-by-16 processor array multiplied by respective weightings, represented by the four signals or beams W₄.

Referring to FIG. 3A, a method for processing data streams or signals by using the system 700 is described below. The sixteen signals A₀ from, e.g., one or more wireless base stations (such as mobile base stations or Wi-Fi base stations) or array elements such as antenna array elements are respectively transmitted into the sixteen 1-to-3 time-domain demultiplexers 50 of the sixteen preprocessor modules 800 a-800 p through, e.g., sixteen parallel signal paths, sixteen parallel wireless channels or sixteen parallel physical channels. Alternatively, the sixteen signals A₀ can be or come from, but not limited to, sixteen digital signals including the four digital signals Z₁, Z₂, Z₃ and Z₄ illustrated in FIG. 2A, including the three digital signals Z₁, Z₂ and Z₃ illustrated in FIG. 2B, including the seven digital signals Z₁-Z₇ illustrated in FIG. 2C, or including the digital signal Z₀ or Z₁ illustrated in FIG. 2D. Each of the sixteen digital signals A₀ can be, but not limited to, a RF digital signal, an IF digital signal, or a real-time digital signal.

Next, referring to FIG. 3A, each of the sixteen 1-to-3 time-domain demultiplexers 50 of the sixteen preprocessor modules 800 a-800 p divides the received signal A₀ having a frequency bandwidth of J sampled at a sampling rate of K into a set of three digital signals X₁, X₂ and X₃, each having a frequency bandwidth of J/3 sampled at a sampling rate of K/3, output in parallel from its three outputs.

Next, referring to FIG. 3A, the sixteen sets of the digital signals X₁, X₂ and X₃ are respectively transmitted in parallel to the sixteen wave-front multiplexers 213 of the sixteen preprocessor modules 800 a-800 p, and at the same time, sixteen digital pilot or diagnostic signals X₄ are respectively transmitted in parallel to the sixteen wave-front multiplexers 213 of the sixteen preprocessor modules 800 a-800 p. Each of the sixteen pilot or diagnostic signals X₄ may have a single frequency and fixed amplitude. Alternatively, each of the sixteen pilot or diagnostic signals X₄ could change based on time or could be any signal known by the system 700. In contrast, the sixteen sets of the three digital signals X₁, X₂ and X₃ input into the sixteen wave-front multiplexers 213 of the sixteen preprocessor modules 800 a-800 p are unknown by the system 700. The sixteen extraneous signals A₀ input into the sixteen preprocessor modules 800 a-800 p are unknown by the system 700.

Referring to FIG. 3A, after sixteen sets of the four signals X₁-X₄ are input into the sixteen wave-front multiplexers 213 of the sixteen preprocessor modules 800 a-800 p, each wave-front multiplexer 213 of the sixteen preprocessor modules 800 a-800 p performs the above-mentioned wave-front multiplexing transformation to process a corresponding set of the four input signals X₁, X₂, X₃ and X₄ into a corresponding set of four linear combinations, each combined with the four input signals X₁, X₂, X₃ and X₄ in the corresponding set multiplied by respective weightings, represented by a corresponding set of the four output signals Y₁, Y₂, Y₃ and Y₄ each having a frequency bandwidth of J/3 sampled at a sampling rate of K/3 Next, the sixteen wave-front multiplexers 213 of the sixteen preprocessor modules 800 a-800 p output the sixteen sets of the four digital signals Y₁, Y₂, Y₃ and Y₄ to the four narrow DBFN modules 801 a-801 d through, e.g., multiple parallel signal paths, multiple parallel physical channels or multiple parallel wireless channels.

For example, the wave-front multiplexer 213 of the preprocessor module 800 a outputs a set of the four digital signals Y₁, Y₂, Y₃ and Y₄ to the four narrow DBFN modules 801 a-801 d through, e.g., four parallel signal paths, four parallel physical channels or four parallel wireless channels. The wave-front multiplexer 213 of the preprocessor modules 800 b outputs another set of the four digital signals Y₁, Y₂, Y₃ and Y₄ to the four narrow DBFN modules 801 a-801 d through, e.g., four parallel signal paths, four parallel physical channels or four parallel wireless channels. The wave-front multiplexer 213 of the preprocessor modules 800 c outputs another set of the four digital signals Y₁, Y₂, Y₃ and Y₄ to the four narrow DBFN modules 801 a-801 d through, e.g., four parallel signal paths, four parallel physical channels or four parallel wireless channels. The wave-front multiplexer 213 of the preprocessor modules 800 d outputs the other set of the four digital signals Y₁, Y₂, Y₃ and Y₄ to the four narrow DBFN modules 801 a-801 d through, e.g., four parallel signal paths, four parallel physical channels or four parallel wireless channels. Thereby, the sixteen digital signals Y₁ from the sixteen preprocessor modules 800 a-800 p are sent to the narrowband DBFN module 801 a through, e.g., sixteen parallel signal paths, sixteen parallel physical channels or sixteen parallel wireless channels. The sixteen digital signals Y₂ from the sixteen preprocessor modules 800 a-800 p are sent to the narrowband DBFN module 801 b through, e.g., sixteen parallel signal paths, sixteen parallel physical channels or sixteen parallel wireless channels. The sixteen digital signals Y₃ from the sixteen preprocessor modules 800 a-800 p are sent to the narrowband DBFN module 801 c through, e.g., sixteen parallel signal paths, sixteen parallel physical channels or sixteen parallel wireless channels. The sixteen digital signals Y₄ from the sixteen preprocessor modules 800 a-800 p are sent to the narrowband DBFN module 801 d through, e.g., sixteen parallel signal paths, sixteen parallel physical channels or sixteen parallel wireless channels.

Next, referring to FIG. 3A, the narrowband DBFN module 801 a processes the sixteen input signals Y₁ from the sixteen preprocessor modules 800 a-800 p and generates the four digital signals or beams W₁ that are four individual linear combinations, each combined with the sixteen input signals Y₁, output from the sixteen wave-front multiplexers 213 of the sixteen preprocessor modules 800 a-800 p, multiplied by respective weightings and outputs the four digital signals or beams W₁, each having a frequency bandwidth of J/3 sampled at a sampling rate of K/3, to the four equalizers 231 of the four post-processor modules 802 a-802 d, respectively. The narrowband DBFN module 801 b processes the sixteen input signals Y₂ from the sixteen preprocessor modules 800 a-800 p and generates the four digital signals or beams W₂ that are four individual linear combinations, each combined with the sixteen input signals Y₂, output from the sixteen wave-front multiplexers 213 of the sixteen preprocessor modules 800 a-800 p, multiplied by respective weightings and outputs the four digital signals or beams W₂, each having a frequency bandwidth of J/3 sampled at a sampling rate of K/3, to the four equalizers 231 of the four post-processor modules 802 a-802 d, respectively. The narrowband DBFN module 801 c processes the sixteen input signals Y₃ from the sixteen preprocessor modules 800 a-800 p and generates the four digital signals or beams W₃ that are four individual linear combinations, each combined with the sixteen input signals Y₃, output from the sixteen wave-front multiplexers 213 of the sixteen preprocessor modules 800 a-800 p, multiplied by respective weightings and outputs the four digital signals or beams W₃, each having a frequency bandwidth of J/3 sampled at a sampling rate of K/3, to the four equalizers 231 of the four post-processor modules 802 a-802 d, respectively. The narrowband DBFN module 801 d processes the sixteen input signals Y₄ from the sixteen preprocessor modules 800 a-800 p and generates the four digital signals or beams W₄ that are four individual linear combinations, each combined with the sixteen input signals Y₄, output from the sixteen wave-front multiplexers 213 of the sixteen preprocessor modules 800 a-800 p, multiplied by respective weightings and outputs the four digital signals or beams W₄, each having a frequency bandwidth of J/3 sampled at a sampling rate of K/3, to the four equalizers 231 of the four post-processor modules 802 a-802 d, respectively. Thereby, each equalizer 231 of the four post-processor modules 802 a-802 d receives a corresponding set of the four input signals W₁, W₂, W₃ and W₄ output from the four narrowband DBFN modules 801 a-801 d.

Next, referring to FIG. 3A, each of the four post-processor module 802 a-802 d may perform the above-mentioned optimizing and equalizing process, illustrated in FIG. 1C, by its equalizer 231 and its optimizer 235 to adjust the amplitudes, phases, and/or time-delays of a corresponding set of the four input signals W₁, W₂, W₃ and W₄ output from the four narrowband DBFN modules 801 a-801 d, and each of the four equalizers 231 of the four post-processor modules 802 a-802 d generates a corresponding set of the four equalized signals S₁, S₂, S₃ and S₄ each having a frequency bandwidth of J/3 sampled at a sampling rate of K/3 and outputs the corresponding set of the four equalized signals S₁, S₂, S₃ and S₄ to the corresponding wave-front demultiplexer 232. Each of the equalized digital signals S₁, S₂, S₃ and S₄ in the corresponding set is created by the corresponding equalizer 231 multiplying the corresponding one of the four digital signals W₁, W₂, W₃ and W₄ in the corresponding set by a weighting of the corresponding equalizer 231. For example, each of the four equalized digital signals S₁ is created by the corresponding equalizer 231 multiplying the corresponding digital signal W₁ by a weighting of the corresponding equalizer 231. Each of the four equalized digital signals S₂ is created by the corresponding equalizer 231 multiplying the corresponding digital signal W₂ by a weighting of the equalizer 231. Each of the four equalized digital signals S₃ is created by the corresponding equalizer 231 multiplying the corresponding digital signal W₃ by a weighting of the corresponding equalizer 231. Each of the four equalized digital signals S₄ is created by the corresponding equalizer 231 multiplying the corresponding digital signal W₄ by a weighting of the corresponding equalizer 231.

Next, referring to FIG. 3A, the four sets of the four equalized digital signals S₁, S₂, S₃ and S₄ in the four post-processor modules 802 a-802 d are respectively transmitted in parallel into the four wave-front demultiplexers 232 of the four post-processor modules 802 a-802 d through multiple parallel signal paths or multiple parallel wireless or physical channels between the four equalizers 231 of the four post-processor modules 802 a-802 d and the four wave-front demultiplexers 232 of the four post-processor modules 802 a-802 d.

Next, referring to FIG. 3A, each wave-front demultiplexer 232 of the four post-processor modules 802 a-802 d performs the above wave-front demultiplexing transform to process the corresponding set of the four equalized digital signals S₁, S₂, S₃ and S₄ into a corresponding set of four linear combinations, each combined with the four equalized digital signals S₁, S₂, S₃ and S₄ in the corresponding set multiplied by respective weightings, represented by a corresponding set of the four digital signals Z₁, Z₂, Z₃ and Z₄, each having a frequency bandwidth of J/3 sampled at a sampling rate of K/3, output in parallel from said each wave-front demultiplexer 232 of the four post-processor modules 802 a-802 d.

Each of the four wave-front demultiplexers 232 of the four post-processor modules 802 a outputs the corresponding signal Z₄ to the corresponding optimizer 235, and each of the four optimizers 235 of the four post-processor modules 802 a-802 d generates the control signal CS and sends the control signal CS to the corresponding equalizer 231 to adjust the weightings of the corresponding equalizer 231, as illustrated in FIG. 1C.

At the same time, the four wave-front demultiplexers 232 of the four post-processor modules 802 a-802 d output in parallel four sets of the three digital signals Z₁, Z₂ and Z₃ to the four 3-to-1 time-domain multiplexers 51 of the four post-processor module 802 a-802 d, and each 3-to-1 time-domain multiplexer 51 of the four post-processor modules 802 a-802 d combines or integrates the corresponding set of the three parallel signals Z₁, Z₂ and Z₃ into a corresponding single signal or beam B₀ having a frequency bandwidth of J sampled at a sampling rate of K and outputs the signal B₀ from its output.

Thereby, referring to FIG. 3A, the sixteen input signals A₀ are respectively processed by the sixteen preprocessor modules 800 a-800 p, and each of the sixteen preprocessor modules 800 a-800 p outputs a set of the four digital signals Y₁, Y₂, Y₃ and Y₄ to the four narrowband DBFN modules 801 a-801 d. The sixteen sets of the four digital signals Y₁, Y₂, Y₃ and Y₄ are processed by the four narrowband DBFN modules 801 a-801 d, and the four narrowband DBFN modules 801 a-801 d output four sets of the four digital signals or beams W₁-W₄ to the four post-processor modules 802 a-802 d. The four sets of the four digital signals or beams W₁-W₄ are respectively processed by the four post-processor modules 802 a-802 d, and each of the four post-processor modules 802 a-802 d outputs the digital signal or beam B₀.

Referring to FIG. 3A, the broadband DBFN system 700 can process the sixteen input signals A₀ each having a bandwidth greater than that of each of the signals Y₁, Y₂, Y₃ and Y₄ output from the sixteen preprocessor modules 800 a-800 p, greater than that of each of the signals W₁, W₂, W₃ and W₄ input into the four post-processor modules 802 a-802 d, and substantially equal to each of the four signals B₀ output from the four postprocessor modules 802 a-802 d. The broadband DBFN system 700 can process the sixteen input signals A₀ each sampled at a greater sampling rate than each of the signals Y₁, Y₂, Y₃ and Y₄ output from the sixteen preprocessor modules 800 a-800 p is sampled and than each of the signals W₁, W₂, W₃ and W₄ input into the four post-processor modules 802 a-802 d is sampled. The broadband DBFN system 700 can process the sixteen input signals A₀ each sampled at the same sampling rate as each signal B₀ output from the four postprocessor modules 802 a-802 d is sampled.

Referring to FIG. 3A, each of the signals A₀, S₁-S₄, Z₁-Z₄ and B₀ can be, but not limited to, sampled at least twice or triple its (maximum) frequency or bandwidth. Each signal A₀ may have a frequency, such as maximum frequency, or bandwidth at least three times higher than that of each of the signals X₁-X₄, Y₁-Y₄, S₁-S₄ and Z₁-Z₄ and substantially equal to that of each signal B₀ Each of the four signals B₀ may have a frequency, such as maximum frequency, or bandwidth at least three times higher than that of each of the signals X₁-X₄, Y₁-Y₄, W₁-W₄, S₁-S₄ and Z₁-Z₄.

Referring to FIG. 3A, the signal A₀ input to the preprocessor module 800 b may have a frequency, such as maximum frequency, equal to or lower than that of the signal A₀ input to the preprocessor module 800 a. The signal A₀ input to the preprocessor module 800 c may have a frequency, such as maximum frequency, equal to or lower than those of the signals A₀ input to the preprocessor module 800 a and 800 b, respectively. The signal A₀ input to the preprocessor module 800 d may have a frequency, such as maximum frequency, equal to or lower than those of the signals A₀ input to the preprocessor module 800 a, 800 b and 800 c, respectively. Thereby, all of the sixteen signals A₀ input to the sixteen preprocessor modules 800 a-800 p may have the same (maximum) frequency or bandwidth and all of the sixteen signals A₀ input to the sixteen preprocessor modules 800 a-800 p may be sampled at the same sampling rate. Alternatively, the sixteen signals A₀ input to the sixteen preprocessor modules 800 a-800 p may have different (maximum) frequencies or bandwidths from one another, and the sixteen signals A₀ input to the sixteen preprocessor modules 800 a-800 p may be sampled at different sampling rates from one another.

Alternatively, the system 700 may include more than sixteen preprocessor modules to receive and process more than sixteen input signals and may also include more than four post-processor modules to generate more than four output signals or beams. Moreover, each of the four narrowband DBFN modules 801 a-801 d of the system 700 can process more than sixteen individual digital signals from the more than sixteen preprocessor modules to create more than four digital coherent signals or beams.

Alternatively, the system 700 may include at least two preprocessor modules to receive and process at least two input signals and may also include at least one post-processor module to generate at least one output signal or beam. Moreover, each of the four narrowband DBFN modules 801 a-801 d of the system 700 can process at least two individual digital signals from the at least two preprocessor modules to create at least one digital signal or beam.

Alternatively, the system 700 can include more than four narrowband DBFN modules, such as eight narrowband DBFN modules 801 a-801 h illustrated in FIG. 3C (the four narrowband DBFN modules 801 d-801 g are not shown in FIG. 3C). In this case, each of the preprocessor modules of the system 700 may include a 1-to-M time-domain demultiplexer and a H-input and H-output wave-front multiplexer, and each of the post-processor modules of the system 700 may include a M-to-1 time-domain multiplexer, an equalizer, a I-input and I-output wave-front demultiplexer, and an optimizer, where H is an integer equal to the total number of the narrowband DBFN modules of the system 700, I is an integer equal to the integer H, and M is an integer less than or equal to each of the integers H and I.

The 1-to-M time-domain demultiplexer denotes that it can divide an input signal, having a frequency bandwidth of J sampled at a sampling rate of K, into the number M of output signals, each having a frequency bandwidth of J/M sampled at a sampling rate of K/M. For example, the 1-to-M time-domain demultiplexer can be, but not limited to, a 1-to-7 time-domain demultiplexer 50 shown in FIG. 3C, and the 1-to-7 time-domain demultiplexer 50 denotes that it can divide an input signal, having a frequency bandwidth of J sampled at a sampling rate of K, into seven output signals, each having a frequency bandwidth of J/7 sampled at a sampling rate of K/7.

The M-to-1 time-domain multiplexer denotes that it can combine or integrate the number M of input signals, each having a frequency bandwidth of J/M sampled at a sampling rate of K/M, into an output signal having a frequency bandwidth of J sampled at a sampling rate of K. For example, the M-to-1 time-domain multiplexer can be, but not limited to, a 7-to-1 time-domain multiplexer 51 shown in FIG. 3C, and the 7-to-1 time-domain multiplexer 51 denotes that it can combine or integrate seven input signals, each having a frequency bandwidth of J/7 sampled at a sampling rate of K/7, into an output signal having a frequency bandwidth of J sampled at a sampling rate of K.

The H-input and H-output wave-front multiplexer denotes that it has the number H of inputs to receive the number H of input signals and the number H of outputs to output the number H of linear combinations, each combined with the number H of the input signals multiplied by respective weightings. For example, the H-input and H-output wave-front multiplexer can be, but not limited to, an eight-input and eight-output wave-front multiplexer 213 illustrated in FIG. 3C, and the eight-input and eight-output wave-front multiplexer 213 denotes that it has eight inputs to receive eight input signals X₁-X₈ and eight outputs to output eight linear combinations, each combined with the eight input signals X₁-X₈ multiplied by respective weightings, represented by eight output signals Y₁-Y₈, which can be referred to as the description illustrated in FIG. 1D. In this case, the number of H is equal to 8. The wavefront multiplexer 213 illustrated in FIG. 3C may include 8*8 computing units and eight summing processors, wherein the computing units form a processor array with eight rows and eight columns. The eight input signals X₁-X₈ can be received by the computing units in the respective eight columns in the processor array. Upon receiving the eight input signals X₁-X₈, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The eight summing processors can output the eight signals Y₁-Y₈ each combined with the weighted signals output from the computing units in a corresponding one of the eight rows in the processor array.

The I-input and I-output wave-front demultiplexer denotes that it has the number I of inputs to receive the number I of input signals and the number I of outputs to output the number I of linear combinations, each combined with the number I of the input signals multiplied by respective weightings. For example, the I-input and I-output wave-front demultiplexer can be, but not limited to, an eight-input and eight-output wave-front demultiplexer 232 illustrated in FIG. 3C, and the eight-input and eight-output wave-front demultiplexer 232 denotes that it has eight inputs to receive eight input signals S₁-S₈ and eight outputs to output eight linear combinations, each combined with the eight input signals S₁-S₈ multiplied by respective weightings, represented by eight output signals Z₁-Z₈, which can be referred to as the description illustrated in FIG. 1E. In this case, the number of I is equal to 8. The wavefront demultiplexer 232 illustrated in FIG. 3C may include 8*8 computing units and eight summing processors, wherein the computing units form a processor array with eight rows and eight columns. The input signals S₁-S₈ can be received by the computing units in the respective eight columns in the processor array. Upon receiving the input signals S₁-S₈, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The eight summing processors can output the eight signals Z₁-Z₈ each combined with the weighted signals output from the computing units in a corresponding one of the eight rows in the processor array.

Referring to FIG. 3C, the system 700 may include sixteen preprocessor modules 800 a-800 p having the same architecture as one another, the eight narrowband DBFN modules 801 a-801 h having the same architecture as one another, and four post-processor modules 802 a-802 d having the same architecture as one another. Each of the sixteen preprocessor modules 800 a-800 p of the system 700 includes the 1-to-7 time-domain demultiplexer 50 and the eight-input and eight-output wave-front multiplexer 213, and each of the four post-processor modules 802 a-802 d of the system 700 includes the 7-to-1 time-domain multiplexer 51, the equalizer 231, the eight-input and eight-output wave-front demultiplexer 232, and the optimizer 235. Each of the 1-to-7 time-domain demultiplexers 50 of the sixteen preprocessor modules 800 a-800 p includes an input and seven outputs and can divide an input signal having a frequency bandwidth of J sampled at a sampling rate of K, input to its input, into seven output signals each having a frequency bandwidth of J/7 sampled at a sampling rate of K/7, output from its seven outputs. Each of the 7-to-1 time-domain multiplexers 51 of the four post-processor modules 802 a-802 d includes seven inputs and an output and can combine or integrate seven input signals each having a frequency bandwidth of J/7 sampled at a sampling rate of K/7, input to its seven inputs, into an output signal having a frequency bandwidth of J sampled at a sampling rate of K, output from its output. The eight narrowband DBFN modules 801 a-801 h can process sixteen sets of the eight signals Y₁-Y₈, each having a frequency bandwidth of J/7 sampled at a sampling rate of K/7, output from the sixteen preprocessor modules 800 a-800 p so as to output four sets of the eight digital signals or beams W₁-W₈, each having a frequency bandwidth of J/7 sampled at a sampling rate of K/7, to the four post-processor modules 802 a-802 d. Each of the eight narrowband DBFN modules 801 a-801 h illustrated herein has the same architecture as the narrowband DBFN module 801 a illustrated in FIG. 3A.

A method for processing data streams or signals by using the system 700 illustrated in FIG. 3C is described below. Sixteen different signals A₀ from, e.g., one or more wireless base stations (such as mobile base stations or Wi-Fi base stations) or array elements such as antenna array elements are respectively transmitted into the sixteen 1-to-7 time-domain demultiplexers 50 of the sixteen preprocessor modules 800 a-800 p through, e.g., sixteen parallel signal paths, sixteen parallel wireless channels or sixteen parallel physical channels. Alternatively, the sixteen signals A₀ can be or come from, but not limited to, sixteen digital signals including the four digital signals Z₁, Z₂, Z₃ and Z₄ illustrated in FIG. 2A, including the three digital signals Z₁, Z₂ and Z₃ illustrated in FIG. 2B, including the seven digital signals Z₁-Z₇ illustrated in FIG. 2C, or including the digital signal Z₀ or Z₁ illustrated in FIG. 2D. Each of the sixteen digital signals A₀ can be, but not limited to, a RF digital signal, an IF digital signal, or a real-time digital signal. In FIG. 3C, the signals with the same reference number may not represent the signals carrying the same information.

Next, referring to FIG. 3C, each of the sixteen 1-to-7 time-domain demultiplexers 50 of the sixteen preprocessor modules 800 a-800 p divides the received signal A₀ having a frequency bandwidth of J sampled at a sampling rate of K into a set of seven digital signals X₁-X₇ each having a frequency bandwidth of J/7 sampled at a sampling rate of K/7 and outputs the set of the seven digital signals X₁-X₇ from its seven outputs. The four signals X₃-X₆ are not shown in FIG. 3C. Next, the sixteen sets of the seven digital signals X₁-X₇, output from the sixteen 1-to-7 time-domain demultiplexers 50 of the sixteen preprocessor modules 800 a-800 p, are respectively transmitted in parallel to the sixteen wave-front multiplexers 213 of the sixteen preprocessor modules 800 a-800 p, and at the same time, sixteen digital pilot or diagnostic signals X₈ are respectively transmitted in parallel to the sixteen wave-front multiplexers 213 of the sixteen preprocessor modules 800 a-800 p. Each of the sixteen pilot or diagnostic signals X₈ may have a single frequency and fixed amplitude. Alternatively, each of the sixteen pilot or diagnostic signals X₈ could change based on time or could be any signal known by the system 700. In contrast, the sixteen sets of the seven digital signals X₁-X₇, input into the sixteen wave-front multiplexers 213 of the sixteen preprocessor modules 800 a-800 p, are unknown by the system 700. The sixteen extraneous signals A₀ input into the sixteen preprocessor modules 800 a-800 p are unknown by the system 700.

Referring to FIG. 3C, after sixteen sets of the eight signals X₁-X₈ are sent into the sixteen wave-front multiplexers 213 of the sixteen preprocessor modules 800 a-800 p, each wave-front multiplexer 213 of the sixteen preprocessor modules 800 a-800 p performs the above wave-front multiplexing transform to process a corresponding set of the eight input signals X₁-X₈ into a corresponding set of eight linear combinations, each combined with the eight input signals X₁-X₈ in the corresponding set multiplied by respective weightings, represented by a corresponding set of the eight output signals Y₁-Y₈ each having a frequency bandwidth of J/7 sampled at a sampling rate of K/7. The four signals Y₄-Y₇ are not shown in FIG. 3C. Thereby, the sixteen wave-front multiplexers 213 of the sixteen preprocessor modules 800 a-800 p output the sixteen sets of the eight digital signals Y₁-Y₈ to the eight narrow DBFN modules 801 a-801 h through, e.g., multiple parallel signal paths, multiple parallel physical channels or multiple parallel wireless channels.

Each of the sixteen wave-front multiplexers 213 of the sixteen preprocessor modules 800 a-800 p outputs the corresponding set of the eight digital signals Y₁-Y₈ to the eight narrow DBFN modules 801 a-801 h through, e.g., eight parallel signal paths, eight parallel physical channels or eight parallel wireless channels. Thereby, the sixteen signals Y₁ from the sixteen preprocessor modules 800 a-800 p are sent to the narrowband DBFN module 801 a through, e.g., sixteen parallel signal paths, sixteen parallel physical channels or sixteen parallel wireless channels. The sixteen signals Y₂ from the sixteen preprocessor modules 800 a-800 p are sent to the narrowband DBFN module 801 b through, e.g., sixteen parallel signal paths, sixteen parallel physical channels or sixteen parallel wireless channels. The sixteen signals Y₃ from the sixteen preprocessor modules 800 a-800 p are sent to the narrowband DBFN module 801 c through, e.g., sixteen parallel signal paths, sixteen parallel physical channels or sixteen parallel wireless channels. The sixteen signals Y₄ from the sixteen preprocessor modules 800 a-800 p are sent to the narrowband DBFN module 801 d through, e.g., sixteen parallel signal paths, sixteen parallel physical channels or sixteen parallel wireless channels. The sixteen signals Y₅ from the sixteen preprocessor modules 800 a-800 p are sent to the narrowband DBFN module 801 e through, e.g., sixteen parallel signal paths, sixteen parallel physical channels or sixteen parallel wireless channels. The sixteen signals Y₆ from the sixteen preprocessor modules 800 a-800 p are sent to the narrowband DBFN module 801 f through, e.g., sixteen parallel signal paths, sixteen parallel physical channels or sixteen parallel wireless channels. The sixteen signals Y₇ from the sixteen preprocessor modules 800 a-800 p are sent to the narrowband DBFN module 801 g through, e.g., sixteen parallel signal paths, sixteen parallel physical channels or sixteen parallel wireless channels. The sixteen signals Y₈ from the sixteen preprocessor modules 800 a-800 p are sent to the narrowband DBFN module 801 h through, e.g., sixteen parallel signal paths, sixteen parallel physical channels or sixteen parallel wireless channels.

Next, referring to FIG. 3C, the eight narrowband DBFN modules 801 a-801 h process the sixteen sets of the eight digital signals Y₁-Y₈ output from the sixteen preprocessor modules 800 a-800 p and generate four sets of the eight signals or beams W₁-W₈. The four digital signals or beams W₁ output from the narrowband DBFN module 801 a are four individual linear combinations, each combined with the sixteen input signals Y₁ multiplied by respective weightings. The four digital signals or beams W₂ output from the narrowband DBFN module 801 b are four individual linear combinations, each combined with the sixteen input signals Y₂ multiplied by respective weightings. The four digital signals or beams W₃ output from the narrowband DBFN module 801 c are four individual linear combinations, each combined with the sixteen input signals Y₃ multiplied by respective weightings. The four digital signals or beams W₄ output from the narrowband DBFN module 801 d are four individual linear combinations, each combined with the sixteen input signals Y₄ multiplied by respective weightings. The four digital signals or beams W₅ output from the narrowband DBFN module 801 e are four individual linear combinations, each combined with the sixteen input signals Y₅ multiplied by respective weightings. The four digital signals or beams W₆ output from the narrowband DBFN module 801 f are four individual linear combinations, each combined with the sixteen input signals Y₆ multiplied by respective weightings. The four digital signals or beams W₇ output from the narrowband DBFN module 801 g are four individual linear combinations, each combined with the sixteen input signals Y₇ multiplied by respective weightings. The four digital signals or beams W₈ output from the narrowband DBFN module 801 h are four individual linear combinations, each combined with the sixteen input signals Y₈ multiplied by respective weightings.

Next, referring to FIG. 3C, the eight DBFN modules 801 a-801 h output the four sets of the eight signals or beams W₁-W₈ to the four post-processor modules 802 a-802 d. The DBFN module 801 a outputs the four signals or beams W₁, each having a frequency bandwidth of J/7 sampled at a sampling rate of K/7, to the four equalizers 231 of the four post-processor modules 802 a-802 d, respectively. The DBFN module 801 b outputs the four signals or beams W₂, each having a frequency bandwidth of J/7 sampled at a sampling rate of K/7, to the four equalizers 231 of the four post-processor modules 802 a-802 d, respectively. The DBFN module 801 c outputs the four signals or beams W₃, each having a frequency bandwidth of J/7 sampled at a sampling rate of K/7, to the four equalizers 231 of the four post-processor modules 802 a-802 d, respectively. The DBFN module 801 d outputs the four signals or beams W₄, each having a frequency bandwidth of J/7 sampled at a sampling rate of K/7, to the four equalizers 231 of the four post-processor modules 802 a-802 d, respectively. The DBFN module 801 e outputs the four signals or beams W₅, each having a frequency bandwidth of J/7 sampled at a sampling rate of K/7, to the four equalizers 231 of the four post-processor modules 802 a-802 d, respectively. The DBFN module 801 f outputs the four signals or beams W₆, each having a frequency bandwidth of J/7 sampled at a sampling rate of K/7, to the four equalizers 231 of the four post-processor modules 802 a-802 d, respectively. The DBFN module 801 g outputs the four signals or beams W₇, each having a frequency bandwidth of J/7 sampled at a sampling rate of K/7, to the four equalizers 231 of the four post-processor modules 802 a-802 d, respectively. The DBFN module 801 h outputs the four signals or beams W₈, each having a frequency bandwidth of J/7 sampled at a sampling rate of K/7, to the four equalizers 231 of the four post-processor modules 802 a-802 d, respectively.

Next, referring to FIG. 3C, each of the four post-processor modules 802 a-802 d may perform an optimizing and equalizing process by its equalizer 231 and its optimizer 235 to adjust the amplitudes, phases, and/or time-delays of the eight signals W₁-W₈ output from its eight narrowband DBFN modules 801 a-801 h, and each of the four equalizers 231 of the four post-processor modules 802 a-802 d generates a corresponding set of the eight equalized signals S₁-S₈ each having a frequency bandwidth of J/7 sampled at a sampling rate of K/7 and outputs the corresponding set of the eight equalized signals S₁-S₈ to the corresponding wave-front demultiplexer 232. The signals S₃-S₇ are not shown in FIG. 3C. Each of the equalized digital signals S₁-S₈ in the corresponding set is created by the corresponding equalizer 231 multiplying the corresponding one of the eight digital signals W₁-W₈ in the corresponding set by a weighting of the corresponding equalizer 231. For example, each of the four equalized digital signals S₁ is created by the corresponding equalizer 231 multiplying the corresponding digital signal W₁ by a weighting of the corresponding equalizer 231.

Next, referring to FIG. 3C, the four sets of the eight equalized digital signals S₁-S₈ in the four post-processor modules 802 a-802 d are respectively transmitted in parallel into the four wave-front demultiplexers 232 of the four post-processor modules 802 a-802 d through multiple parallel signal paths or multiple parallel wireless or physical channels between the four equalizers 231 of the four post-processor modules 802 a-802 d and the four wave-front demultiplexers 232 of the four post-processor modules 802 a-802 d.

Next, referring to FIG. 3C, each of the four wave-front demultiplexers 232 of the four post-processor modules 802 a-802 d performs the above wave-front demultiplexing transform to process the corresponding set of the eight equalized digital signals S₁-S₈ into a corresponding set of eight linear combinations, each combined with the eight equalized digital signals S₁-S₈ in the corresponding set multiplied by respective weightings, represented by the eight digital signals Z₁-Z₈, each having a frequency bandwidth of J/7 sampled at a sampling rate of K/7, output in parallel from said each of the four wave-front demultiplexers 232 of the four post-processor modules 802 a-802 d.

Next, referring to FIG. 3C, each of the four wave-front demultiplexers 232 of the four post-processor modules 802 a outputs the corresponding signal Z₈ to the corresponding optimizer 235, and each optimizer 235 of the four post-processor modules 802 a-802 d generates a control signal CS and sends the control signal CS to the corresponding equalizer 231 to adjust the weightings of the corresponding equalizer 231, as illustrated in FIG. 1C.

At the same time, the four wave-front demultiplexers 232 of the four post-processor modules 802 a-802 d output in parallel four sets of the seven digital signals Z₁-Z₇ to the four 7-to-1 time-domain multiplexers 51 of the four post-processor module 802 a-802 d, and each of the four 7-to-1 time-domain multiplexers 51 of the four post-processor modules 802 a-802 d combines or integrates the corresponding set of the seven parallel signals Z₁-Z₇ into a corresponding single signal or beam B₀, having a frequency bandwidth of J sampled at a sampling rate of K, and outputs the signal B₀ from its output.

Thereby, referring to FIG. 3C, the sixteen input signals A₀ are respectively processed by the sixteen preprocessor modules 800 a-800 p, and each of the sixteen preprocessor modules 800 a-800 p outputs a set of the eight digital signals Y₁-Y₈ to the eight narrowband DBFN modules 801 a-801 h. The sixteen sets of the eight digital signals Y₁-Y₈ are processed by the eight narrowband DBFN modules 801 a-801 h, and the eight narrowband DBFN modules 801 a-801 h output four sets of the eight digital signals or beams W₁-W₈ to the four post-processor modules 802 a-802 d. The four sets of the eight digital signals or beams W₁-W₈ are respectively processed by the four post-processor modules 802 a-802 d, and each of the four post-processor modules 802 a-802 d outputs the digital signal or beam B₀.

Referring to FIG. 3C, the broadband DBFN system 700 can process the sixteen input signals A₀, each having a bandwidth greater than that of each of the signals Y₁-Y₈ output from the preprocessor modules 800 a-800 p, greater than that of each of the signals W₁-W₈ input into the four post-processor modules 802 a-802 d, and substantially equal to each of the four signals B₀ output from the four post-processor modules 802 a-802 d. The broadband DBFN system 700 can process the sixteen input signals A₀ each sampled at a greater sampling rate than each of the signals Y₁-Y₈ output from the sixteen preprocessor modules 800 a-800 p is sampled and than each of the signals W₁-W₈ input into the four post-processor modules 802 a-802 d is sampled. The broadband DBFN system 700 can process the sixteen input signals A₀ each sampled at the same sampling rate as each signal B₀ output from the postprocessor modules 802 a-802 d is sampled.

Referring to FIG. 3C, each of the signals A₀, X₁-X₈, Y₁-Y₈, W₁-W₈, S₁-S₈, Z₁-Z₈ and B₀ can be, but not limited to, sampled at least twice or triple its (maximum) frequency or bandwidth. Each signal A₀ may have a frequency, such as maximum frequency, or bandwidth substantially seven times higher than that of each of the signals X₁-X₈, Y₁-Y₈, W₁-W₈, S₁-S₈ and Z₁-Z₈ and substantially equal to that of each signal B₀. All of the signals A₀ input to the preprocessor modules 800 a-800 p may have the same maximum frequency or bandwidth, and all of the signals A₀ input to the preprocessor modules 800 a-800 p may be sampled at the same sampling rate. Alternatively, the signals A₀ input to the preprocessor modules 800 a-800 p may have different maximum frequencies or bandwidths from one another, and the signals A₀ input to the preprocessor modules 800 a-800 p may be sampled at different sampling rates from one another.

Alternatively, the system 700 can include more than eight narrowband DBFN modules, such as sixteen narrowband DBFN modules 801 a-801 p illustrated in FIG. 3D. The narrowband DBFN modules 801 d-801 o are not shown in FIG. 3D. Moreover, the system 700 can include more than sixteen preprocessor modules, such as thirty-two preprocessor modules 800 illustrated in FIG. 3D, and can include more than or equal to two post-processor modules, such as four post-processor modules 802 illustrated in FIG. 3D. Each of the preprocessor modules of the system 700 may include a 1-to-M time-domain demultiplexer, a H-input and H-output wave-front multiplexer, and multiple U-to-1 time-domain multiplexers, and each of the post-processor modules of the system 700 may include a M-to-1 time-domain multiplexer, an equalizer, a I-input and I-output wave-front demultiplexer, an optimizer, and multiple 1-to-U time-domain demultiplexers, where H is an integer, I is an integer equal to the integer H, M is an integer less than or equal to each of the integers H and I, and U is an integer equal to the total number of the narrowband DBFN modules of the system 700 and less than each of the integers H, I and M. A signal input into the 1-to-M time-domain demultiplexer may have the bandwidth or (maximum) frequency substantially M times greater than that of each of signals output from the 1-to-M time-domain demultiplexer. A signal output from the M-to-1 time-domain multiplexer may have the bandwidth or (maximum) frequency substantially M times greater than that of each of signals input into the M-to-1 time-domain multiplexer. A signal input into the 1-to-U time-domain demultiplexer may have the bandwidth or (maximum) frequency substantially U times greater than that of each of signals output from the 1-to-U time-domain demultiplexer. A signal output from the U-to-1 time-domain multiplexer may have the bandwidth or (maximum) frequency substantially U times greater than that of each of signals input into the U-to-1 time-domain multiplexer.

For example, the 1-to-M time-domain demultiplexer can be, but not limited to, a 1-to-250 time-domain demultiplexer 50 illustrated in FIG. 3E, and the 1-to-250 time-domain demultiplexer 50 denotes that it can divide an input signal A₀, having a frequency bandwidth of J sampled at a sampling rate of K, into two-hundred-and-fifty output signals X₁-X₂₅₀, each having a frequency bandwidth of J/250 sampled at a sampling rate of K/250. The signal A₀ input into the 1-to-250 time-domain demultiplexer 50 may have the bandwidth or (maximum) frequency substantially two-hundred-and-fifty times greater than that of each of the two-hundred-and-fifty signals X₁-X₂₅₀ output from the 1-to-250 time-domain demultiplexer 50. The M-to-1 time-domain multiplexer can be, but not limited to, a 250-to-1 time-domain multiplexer 51 illustrated in FIG. 3F, and the 250-to-1 time-domain multiplexer 51 denotes that it can combine or integrate two-hundred-and-fifty input signals Z₁-Z₂₅₀, each having a frequency bandwidth of J/250 sampled at a sampling rate of K/250, into an output signal B₀ having a frequency bandwidth of J sampled at a sampling rate of K. The signal B₀ output from the 250-to-1 time-domain multiplexer 51 may have the bandwidth or (maximum) frequency substantially two-hundred-and-fifty times greater than that of each of the two-hundred-and-fifty signals Z₁-Z₂₅₀ input into the 250-to-1 time-domain multiplexer 51.

Each of the 1-to-U time-domain demultiplexers denotes that it can divide an input signal, having a frequency bandwidth of E sampled at a sampling rate of F, into the number U of output signals, each having a frequency bandwidth of E/U sampled at a sampling rate of F/U. The number E can be, but not limited to, equal to the number of J multiplied by U, divided by M, and the number F can be, but not limited to, equal to the number of K multiplied by U, divided by M. For example, the 1-to-U time-domain demultiplexers can be, but not limited to, sixteen 1-to-16 time-domain demultiplexers 53 a-53 p shown in FIG. 3F, and each of the sixteen 1-to-16 time-domain demultiplexers 53 a-53 p denotes that it can divide a corresponding one of sixteen input signal M₁-M₁₆, each having a frequency bandwidth of E sampled at a sampling rate of F, into a corresponding set of sixteen ones of two-hundred-and-fifty-six output signals W₁-W₂₅₆, each having a frequency bandwidth of E/16 sampled at a sampling rate of F/16. In this case, as shown in FIG. 3F, the number E is equal to the number of 16*J/250, and the number F is equal to the number of 16*K/250. The thirteen 1-to-16 time-domain demultiplexers 53 c-53 o are not shown in FIG. 3F. Each of sixteen signals M₁-M₁₆ input into the sixteen 1-to-16 time-domain demultiplexers 53 a-53 p may have the bandwidth or (maximum) frequency substantially 16 times greater than that of each of two-hundred-and-fifty-six signals W₁-W₂₅₆ output from the sixteen 1-to-16 time-domain demultiplexers 53 a-53 p.

Each of the U-to-1 time-domain multiplexers denotes that it can combine or integrate the number U of input signals, each having a frequency bandwidth of E/U sampled at a sampling rate of F/U, into an output signal having a frequency bandwidth of E sampled at a sampling rate of F. The number E can be, but not limited to, equal to the number of J multiplied by U, divided by M, and the number F can be, but not limited to, equal to the number of K multiplied by U, divided by M. For example, the U-to-1 time-domain multiplexers can be, but not limited to, sixteen 16-to-1 time-domain multiplexers 52 a-52 p shown in FIG. 3E, and each of the sixteen 16-to-1 time-domain multiplexers 52 a-52 p denotes that it can combine or integrate a corresponding set of sixteen ones of two-hundred-and-fifty-six input signals Y₁-Y₂₅₆, each having a frequency bandwidth of E/16 sampled at a sampling rate of F/16, into a corresponding one of sixteen output signals L₁-L₁₆, each having a frequency bandwidth of E sampled at a sampling rate of F. In this case, as shown in FIG. 3E, the number E is equal to the number of 16*J/250, and the number F is equal to the number of 16*K/250. The thirteen 16-to-1 time-domain multiplexers 52 c-52 o are not shown in FIG. 3E. Each of sixteen signals L₁-L₁₆ output from the sixteen 16-to-1 time-domain multiplexers 52 a-52 p may have the bandwidth or (maximum) frequency substantially 16 times greater than that of each of two-hundred-and-fifty-six signals Y₁-Y₂₅₆ input into the sixteen 16-to-1 time-domain multiplexers 52 a-52 p.

The H-input and H-output wave-front multiplexer can be, but not limited to, a 256-input and 256-output wave-front multiplexer 213 illustrated in FIG. 3E, and the 256-input and 256-output wave-front multiplexer 213 denotes that it has two-hundred-and-fifty-six inputs to receive two-hundred-and-fifty-six input signals X₁-X₂₅₆ and two-hundred-and-fifty-six outputs to output two-hundred-and-fifty-six linear combinations, each combined with the two-hundred-and-fifty-six input signals X₁-X₂₅₆ multiplied by respective weightings, represented by two-hundred-and-fifty-six output signals Y₁-Y₂₅₆, which can be referred to as the description illustrated in FIG. 1D. In this case, the number of H is equal to 256. The wavefront multiplexer 213 illustrated in FIG. 3E may include 256*256 computing units and two-hundred-and-fifty-six summing processors, wherein the computing units form a processor array with two-hundred-and-fifty-six rows and two-hundred-and-fifty-six columns. The input signals X₁-X₂₅₆ can be received by the computing units in the respective two-hundred-and-fifty-six columns in the processor array. Upon receiving the input signals X₁-X₂₅₆, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The two-hundred-and-fifty-six summing processors can output the two-hundred-and-fifty-six signals Y₁-Y₂₅₆ each combined with the weighted signals output from the computing units in a corresponding one of the two-hundred-and-fifty-six rows in the processor array.

The I-input and I-output wave-front demultiplexer can be, but not limited to, a 256-input and 256-output wave-front demultiplexer 232 illustrated in FIG. 3F, and the 256-input and 256-output wave-front demultiplexer 232 denotes that it has two-hundred-and-fifty-six inputs to receive two-hundred-and-fifty-six input signals S₁-S₂₅₆ and two-hundred-and-fifty-six outputs to output two-hundred-and-fifty-six linear combinations, each combined with the two-hundred-and-fifty-six input signals S₁-S₂₅₆ multiplied by respective weightings, represented by two-hundred-and-fifty-six output signals Z₁-Z₂₅₆, which can be referred to as the description illustrated in FIG. 1E. In this case, the number of I is equal to 256. The wavefront demultiplexer 232 illustrated in FIG. 3F may include 256*256 computing units and two-hundred-and-fifty-six summing processors, wherein the computing units form a processor array with two-hundred-and-fifty-six rows and two-hundred-and-fifty-six columns. The input signals S₁-S₂₅₆ can be received by the computing units in the respective two-hundred-and-fifty-six columns in the processor array. Upon receiving the input signals S₁-S₂₅₆, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The two-hundred-and-fifty-six summing processors can output the two-hundred-and-fifty-six signals Z₁-Z₂₅₆ each combined with the weighted signals output from the computing units in a corresponding one of the two-hundred-and-fifty-six rows in the processor array.

The 256-input and 256-output wave-front multiplexer 213 illustrated in FIG. 3E and the 256-input and 256-output wave-front demultiplexer 232 illustrated in FIG. 3F can be 256-to-256 COTS FFT/IFFT chips.

Referring to FIG. 3D, the system 700 may include the thirty-two preprocessor modules 800 having the same architecture as one another, the sixteen narrowband DBFN modules 801 a-801 p having the same architecture as one another, and the four post-processor modules 802 having the same architecture as one another. FIG. 3E shows the architecture of one of the preprocessor modules 800 shown in FIG. 3D. Referring to FIGS. 3D and 3E, each of the thirty-two preprocessor modules 800 includes the 1-to-250 time-domain demultiplexer 50, the 256-input and 256-output wave-front multiplexer 213, and sixteen the 16-to-1 time-domain multiplexers 52 a-52 p. FIG. 3F shows the architecture of one of the post-processor module 802 shown in FIG. 3D. Referring to FIGS. 3D and 3F, each of the four post-processor modules 802 includes the 250-to-1 time-domain multiplexer 51, the sixteen 1-to-16 time-domain demultiplexers 53 a-53 p, the equalizer 231, the 256-input and 256-output wave-front demultiplexer 232, and the optimizer 235. Referring to FIG. 3D, each of the sixteen narrowband DBFN modules 801 a-801 p can process thirty-two different signals from the thirty-two preprocessor modules 800 into four coherent signals or beams and outputs the four coherent signals or beams to the four post-processor modules 802.

Referring to FIG. 3G showing architecture of a narrowband DBFN module in accordance with the present invention, a narrowband DBFN module 801, such as one of the narrowband DBFN modules 801 a-801 p as seen in FIG. 3D, may include a field programmable gate array (FPGA), a fixed-function off-the-shelf digital component or a digital signal processor (DSPs) to process multiple input digital signals, wherein the total number of the input digital signals is Q equal to the total number of preprocessor modules 800 of the system 700, and output multiple linear combinations, each combined with the input digital signals multiplied by respective weightings, wherein the total number of the linear combinations is R equal to the total number of post-processor modules 802 of the system 700. The number of Q could be any number greater than or equal to 2, 4, 8, 16, 32, 64, 128, 256 or 512, and the number of R could be any number greater than or equal to 1, 2, 4, 8, 16, 32, 64, 128, 256 or 512. The DBFN module 801 may include the number R*Q of computing units (CUs) and the number R of summing processors (SPs). The computing units form an R-by-Q processor array with the number Q of columns and the number R of rows. The computing units in each column in the processor array receive a corresponding digital signal output from a corresponding one of the preprocessor modules 800, and thus the number Q of the input digital signals output from the number Q of the preprocessor modules 800 can be received by the computing units in the number Q of respective columns in the processor array. Upon receiving the input digital signals output from the preprocessor modules 800, each of the computing units independently weights its received digital signal to generate a weighted signal. Each of the summing processors provides a means for summing weighted signals generated by the corresponding computing units in same row in the processor array to produce a corresponding digital signal or beam, i.e. beam weighting vector, output to the corresponding post-processor module 802. Accordingly, the number R of the summing processors can output the number R of digital signals or beams, each combined with the weighted signals output from the computing units in a corresponding one of the number R of rows in the processor array. In this case, as seen in FIG. 3D, the number of Q is equal to 32, and the number of R is equal to 4. Each of the narrowband DBFN modules 801 a-801 p may include 4*32 computing units and four summing processors, wherein the computing units in the same column receive a corresponding one of the digital signals L₁-L₁₆ output from a corresponding one of the preprocessor modules 800, each of the summary processors provides a means of summing corresponding signals weighted by the corresponding computing units in the same row and outputs a corresponding one of the digital signals M₁-M₁₆ to a corresponding one of the post-processor modules 802.

In another case, as seen in FIG. 3A, the number of Q is equal to 16, and the number of R is equal to 4. Referring to FIGS. 3A and 3G, each of the narrowband DBFN modules 801 a-801 d may include 4*16 computing units and four summing processors, wherein the computing units in the same column receive a corresponding one of the digital signals Y₁-Y₄ output from a corresponding one of the preprocessor modules 800 a-800 p, each of the summary processors provides a means of summing corresponding signals weighted by the corresponding computing units in the same row and outputs a corresponding one of the digital signals W₁-W₄ to a corresponding one of the post-processor modules 802 a-802 d.

In another case, as seen in FIG. 3C, the number Q is equal to 16, and the number of R is equal to 4. Referring to FIGS. 3C and 3G, each of the narrowband DBFN modules 801 a-801 h may include 4*16 computing units and four summing processors, wherein the computing units in the same column receive a corresponding one of the digital signals Y₁-Y₈ output from a corresponding one of the preprocessor modules 800 a-800 p, each of the summary processors provides a means of summing corresponding signals weighted by the corresponding computing units in the same row and outputs a corresponding one of the digital signals W₁-W₈ to a corresponding one of the post-processor modules 802 a-802 d.

A method for processing data streams or signals by using the system 700 shown in FIG. 3D is described below. Referring to FIGS. 3D and 3E, the thirty-two different signals A₀ from, e.g., one or more wireless base stations (such as mobile base stations or Wi-Fi base stations) or array elements such as antenna array elements are respectively transmitted into the thirty-two 1-to-250 time-domain demultiplexers 50 of the thirty-two preprocessor modules 800 through, e.g., thirty-two parallel signal paths, thirty-two parallel physical channels or thirty-two parallel wireless channels. Alternatively, the thirty-two signals A₀ can be or come from, but not limited to, thirty-two digital signals including the four digital signals Z₁, Z₂, Z₃ and Z₄ illustrated in FIG. 2A, including the three digital signals Z₁, Z₂ and Z₃ illustrated in FIG. 2B, including the seven digital signals Z₁-Z₇ illustrated in FIG. 2C, or including the digital signal Z₀ or Z₁ illustrated in FIG. 2D. Each of the thirty-two digital signals A₀ can be, but not limited to, an IF digital signal, a RF digital signal, or a real-time digital signal. In FIGS. 3D, 3E and 3F, the signals with the same reference number may not represent the signals carrying the same information.

Next, referring to FIGS. 3D and 3E, each of the thirty-two 1-to-250 time-domain demultiplexers 50 of the thirty-two preprocessor modules 800 divides the received signal A₀ having a frequency bandwidth of J sampled at a sampling rate of K into a set of the two-hundred-and-fifty digital signals X₁-X₂₅₀ each having a frequency bandwidth of J/250 sampled at a sampling rate of K/250 and outputs the set of the two-hundred-and-fifty digital signals X₁-X₂₅₀ from its two-hundred-and-fifty outputs. The signals X₃-X₂₄₉ are not shown in FIG. 3E. Next, the thirty-two sets of the two-hundred-and-fifty digital signals X₁-X₂₅₀, output from the thirty-two 1-to-250 time-domain demultiplexers 50 of the thirty-two preprocessor modules 800, are respectively transmitted in parallel to the thirty-two wave-front multiplexers 213 of the thirty-two preprocessor modules 800, and at the same time, thirty-two sets of six digital pilot or diagnostic signals X₂₅₁-X₂₅₆ are respectively transmitted in parallel to the thirty-two wave-front multiplexers 213 of the thirty-two preprocessor modules 800. Each of the pilot or diagnostic signals X₂₅₁₋₂₅₆ may have a single frequency and fixed amplitude. Alternatively, each of the pilot or diagnostic signals X₂₅₁₋₂₅₆ could change based on time or could be any signal known by the system 700. In contrast, the thirty-two sets of the two-hundred-and-fifty digital signals X₁-X₂₅₀ input into the thirty-two wave-front multiplexers 213 of the thirty-two preprocessor modules 800 are unknown by the system 700. The thirty-two extraneous signals A₀ input into the thirty-two preprocessor modules 800 are unknown by the system 700. Each of the thirty-two signals A₀ can be, but not limited to, sampled at least triple as fast as its bandwidth or maximum frequency. For example, if each of the thirty-two signals A₀ has the bandwidth or maximum frequency of 500 MHz, each of the thirty-two signals A₀ can be sampled at 1.5 Gsps (giga-samples per second).

Referring to FIGS. 3D and 3E, after thirty-two sets of the two-hundred-and-fifty-six signals X₁-X₂₅₆ are respectively input into the thirty-two wave-front multiplexers 213 of the thirty-two preprocessor modules 800, each of the thirty-two wave-front multiplexers 213 of the thirty-two preprocessor modules 800 performs the above wave-front multiplexing transform to process a corresponding set of the two-hundred-and-fifty-six signals X₁-X₂₅₆ into a corresponding set of two-hundred-and-fifty-six linear combinations, each combined with the received signals X₁-X₂₅₆ in the corresponding set multiplied by respective weightings, represented by the two-hundred-and-fifty-six digital signals Y₁-Y₂₅₆ and outputs the corresponding set of the two-hundred-and-fifty-six signals Y₁-Y₂₅₆. Each of the digital signals Y₁-Y₂₅₆ may have a bandwidth of J/250 sampled at a sampling rate of K/250. The signals Y₂-Y₁₅, Y₁₈-Y₃₁, Y₃₃-Y₂₄₀, and Y₂₄₂-Y₂₅₅ are not shown in FIG. 3E. Next, in each of the thirty-two preprocessor modules 800, sixteen sets of sixteen ones of the two-hundred-and-fifty-six digital signals Y₁-Y₂₅₆ are respectively transmitted to the sixteen 16-to-1 time-domain multiplexers 52 a-52 p through, e.g., multiple parallel signal paths, multiple parallel physical channels or multiple parallel wireless channels. Each of the signals X₁-X₂₅₀ can be, but not limited to, sampled at least triple as fast as its bandwidth or maximum frequency. For example, if each of the signals X₁-X₂₅₀ has the bandwidth or maximum frequency of 2 MHz, each of the signals X₁-X₂₅₀ can be sampled at 6 Msps (mega samples per second). Each of the signals Y₁-Y₂₅₀ can be, but not limited to, sampled at least triple as fast as its bandwidth or maximum frequency. For example, if each of the signals Y₁-Y₂₅₀ has the bandwidth or maximum frequency of 2 MHz, each of the signals Y₁-Y₂₅₀ can be sampled at 6 Msps.

Next, referring to FIGS. 3D and 3E, in each of the thirty-two preprocessor modules 800, each of the sixteen 16-to-1 time-domain multiplexers 52 a-52 p combines or integrates a corresponding set of the received sixteen ones of the two-hundred-and-fifty-six digital signals Y₁-Y₂₅₆ into a corresponding one of the sixteen digital signals L₁-L₁₆ and outputs the corresponding one of the sixteen signals L₁-L₁₆ to a corresponding one of the sixteen DBFN modules 801 a-801 p. Each of the digital signals L₁-L₁₆ may have a bandwidth of 16*J/250 sampled at a sampling rate of 16*K/250. The twelve DBFN modules 801 d-801 o are not shown in FIG. 3D, and the thirteen signals L₃-L₁₅ are not shown in FIG. 3E. Thereby, thirty-two sets of the sixteen signals L₁-L₁₆ from the thirty-two preprocessor modules 800 are transmitted to the sixteen DBFN modules 801 a-801 p. That is, the sixteen signals L₁-L₁₆ output from each of the thirty-two preprocessor modules 800 are transmitted in parallel to the sixteen narrowband DBFN modules 801 a-801 p, respectively.

Referring to FIGS. 3D and 3E, the thirty-two signals L₁ from the thirty-two preprocessor modules 800 are transmitted in parallel to the DBFN module 801 a through, e.g., thirty-two parallel signal paths, thirty-two parallel physical channels or thirty-two parallel wireless channels. The thirty-two signals L₂ from the thirty-two preprocessor modules 800 are transmitted in parallel to the DBFN module 801 b through, e.g., thirty-two parallel signal paths, thirty-two parallel physical channels or thirty-two parallel wireless channels. The thirty-two signals L₃ from the thirty-two preprocessor modules 800 are transmitted in parallel to the DBFN module 801 c through, e.g., thirty-two parallel signal paths, thirty-two parallel physical channels or thirty-two parallel wireless channels. The thirty-two signals L₁₆ from the thirty-two preprocessor modules 800 are transmitted in parallel to the DBFN module 801 p through, e.g., thirty-two parallel signal paths, thirty-two parallel physical channels or thirty-two parallel wireless channels. Each of the signals L₁-L₁₆ can be, but not limited to, sampled at least triple as fast as its bandwidth or maximum frequency. For example, if each of the signals L₁-L₁₆ has the bandwidth or maximum frequency of 32 MHz, each of the signals L₁-L₁₆ can be sampled at 96 Msps.

Next, referring to FIGS. 3D, 3E and 3F, the sixteen DBFN modules 801 a-801 p process the thirty-two sets of the sixteen signals L₁-L₁₆ from the thirty-two preprocessor modules 800 into four sets of the sixteen signals or beams M₁-M₁₆ and output the four sets of the sixteen signals or beams M₁-M₁₆ to the four post-processor modules 802. The four signals or beams M₁ output from the DBFN module 801 a are four linear combinations, each combined with the thirty-two received signals L₁ multiplied by respective weightings. The four signals or beams M₂ output from the DBFN module 801 b are four linear combinations, each combined with the thirty-two received signals L₂ multiplied by respective weightings. The four signals or beams M₃ output from the DBFN module 801 c are four linear combinations, each combined with the thirty-two received signals L₃ multiplied by respective weightings. The four signals or beams M₄ output from the DBFN module 801 d are four linear combinations, each combined with the thirty-two received signals L₄ multiplied by respective weightings. The four signals or beams M₅ output from the DBFN module 801 e are four linear combinations, each combined with the thirty-two received signals L₅ multiplied by respective weightings. The four signals or beams M₆ output from the DBFN module 801 f are four linear combinations, each combined with the thirty-two received signals L₆ multiplied by respective weightings. The four signals or beams M₇ output from the DBFN module 801 g are four linear combinations, each combined with the thirty-two received signals L₇ multiplied by respective weightings. The four signals or beams Mg output from the DBFN module 801 h are four linear combinations, each combined with the thirty-two received signals L₈ multiplied by respective weightings. The four signals or beams M₉ output from the DBFN module 801 i are four linear combinations, each combined with the thirty-two received signals L₉ multiplied by respective weightings. The four signals or beams M₁₀ output from the DBFN module 801 j are four linear combinations, each combined with the thirty-two received signals L₁₀ multiplied by respective weightings. The four signals or beams M₁₁ output from the DBFN module 801 k are four linear combinations, each combined with the thirty-two received signals L₁₁ multiplied by respective weightings. The four signals or beams M₁₂ output from the DBFN module 801 l are four linear combinations, each combined with the thirty-two received signals L₁₂ multiplied by respective weightings. The four signals or beams M₁₃ output from the DBFN module 801 m are four linear combinations, each combined with the thirty-two received signals L₁₃ multiplied by respective weightings. The four signals or beams M₁₄ output from the DBFN module 801 n are four linear combinations, each combined with the thirty-two received signals L₁₄ multiplied by respective weightings. The four signals or beams M₁₅ output from the DBFN module 801 o are four linear combinations, each combined with the thirty-two received signals L₁₅ multiplied by respective weightings. The four signals or beams M₁₆ output from the DBFN module 801 p are four linear combinations, each combined with the thirty-two received signals L₁₆ multiplied by respective weightings. Each of the digital signals or beams M₁-M₁₆ may have a bandwidth of 16*J/250 sampled at a sampling rate of 16*K/250.

Referring to FIGS. 3D and 3F, the four sets of the sixteen signals or beams M₁-M₁₆ are input into four sets of the sixteen 1-to-16 time-domain demultiplexers 53 a-53 p of the four post-processor modules 802, respectively. That is, in each of the four post-processor modules 802, its sixteen 1-to-16 time-domain demultiplexers 53 a-53 p receive the sixteen corresponding signals or beams M₁-M₁₆, respectively. Each of the signals M₁-M₁₆ can be, but not limited to, sampled at least triple as fast as its bandwidth or maximum frequency. For example, if each of the signals M₁-M₁₆ has the bandwidth or maximum frequency of 32 MHz, each of the signals M₁-M₁₆ can be sampled at 96 Msps.

Next, referring to FIGS. 3D and 3F, the sixteen 1-to-16 time-domain demultiplexers 53 a-53 p in each of the four post-processor modules 802 divide the received sixteen signals or beams M₁-M₁₆ into the corresponding two-hundred-and-fifty-six signals W₁-W₂₅₆ each having a frequency bandwidth of J/250 sampled at a sampling rate of K/250 and output the corresponding two-hundred-and-fifty-six signals W₁-W₂₅₆ to the corresponding equalizer 231. Each of the sixteen 1-to-16 time-domain demultiplexers 53 a-53 p outputs sixteen corresponding ones of the two-hundred-and-fifty-six signals W₁-W₂₅₆. For example, the 1-to-16 time-domain demultiplexer 53 a divides the received signal M₁, having a frequency bandwidth of 16*J/250 sampled at a sampling rate of 16*K/250, into the sixteen output signals W₁-W₁₆, each having a frequency bandwidth of J/250 sampled at a sampling rate of K/250, and outputs the sixteen output signals W₁-W₁₆ to the equalizer 231. The 1-to-16 time-domain demultiplexer 53 b divides the received signal M₂, having a frequency bandwidth of 16*J/250 sampled at a sampling rate of 16*K/250, into the sixteen output signals W₁₇-W₃₂, each having a frequency bandwidth of J/250 sampled at a sampling rate of K/250, and outputs the sixteen output signals W₁₇-W₃₂ to the equalizer 231. The 1-to-16 time-domain demultiplexer 53 p divides the received signal M₁₆, having a frequency bandwidth of 16*J/250 sampled at a sampling rate of 16*K/250, into the sixteen output signals W₂₄₁-W₂₅₆, each having a frequency bandwidth of J/250 sampled at a sampling rate of K/250, and outputs the sixteen output signals W₂₄₁-W₂₅₆ to the equalizer 231.

Next, referring to FIGS. 3D and 3F, each of the four post-processor modules 802 may perform an optimizing and equalizing process by its equalizer 231 and its optimizer 235 to adjust the amplitudes, phases, and/or time-delays of the two-hundred-and-fifty-six signals W₁-W₂₅₆ output from its sixteen 1-to-16 time-domain demultiplexers 53 a-53 p, and each of the four equalizers 231 of the four post-processor modules 802 generates a corresponding set of the two-hundred-and-fifty-six equalized signals S₁-S₂₅₆ each having a frequency bandwidth of J/250 sampled at a sampling rate of K/250 and outputs the corresponding set of the two-hundred-and-fifty-six equalized signals S₁-S₂₅₆ to the corresponding wave-front demultiplexer 232. Each of the equalized digital signals S₁-S₂₅₆ in the corresponding set is created by the corresponding equalizer 231 multiplying the corresponding one of the digital signals W₁-W₂₅₆ in the corresponding by a weighting of the corresponding equalizer 231. For example, each of the four equalized signals S₁ is created by the corresponding equalizer 231 multiplying the corresponding signal W₁ by a weighting of the corresponding equalizer 231. The signals S₃-S₂₅₅ are not shown in FIG. 3F. Each of the signals W₁-W₂₅₆ can be, but not limited to, sampled at least triple as fast as its bandwidth or maximum frequency. For example, if each of the signals W₁-W₂₅₆ has the bandwidth or maximum frequency of 2 MHz, each of the signals W₁-W₂₅₆ can be sampled at 6 Msps. Each of the signals S₁-S₂₅₆ can be, but not limited to, sampled at least triple as fast as its bandwidth or maximum frequency. For example, if each of the signals S₁-S₂₅₆ has the bandwidth or maximum frequency of 2 MHz, each of the signals S₁-S₂₅₆ can be sampled at 6 Msps.

Next, referring to FIGS. 3D and 3F, each of the four wave-front demultiplexers 232 of the four post-processor modules 802 performs the above wave-front demultiplexing transform to process the corresponding set of the two-hundred-and-fifty-six equalized signals S₁-S₂₅₆ into a corresponding set of two-hundred-and-fifty-six linear combinations, each combined with the two-hundred-and-fifty-six equalized signals S₁-S₂₅₆ in the corresponding set multiplied by respective weightings, represented by the two-hundred-and-fifty-six digital signals Z₁-Z₂₅₆ each having a frequency bandwidth of J/250 sampled at a sampling rate of K/250.

Next, referring to FIGS. 3D and 3F, the four wave-front demultiplexers 232 of the four post-processor modules 802 output in parallel four sets of the six digital signals Z₂₅₁-Z₂₅₆ to the four optimizers 235, and each of the four optimizers 235 of the four post-processor modules 802 generates a control signal CS and sends the control signal CS to the corresponding equalizer 231 to adjust the weightings of the corresponding equalizer 231, as illustrated in FIG. 1C.

At the same time, the four wave-front demultiplexers 232 of the four post-processor modules 802 output in parallel four sets of the two-hundred-and-fifty signals Z₁-Z₂₅₀ to the four 250-to-1 time-domain multiplexers 51, and each of the four 250-to-1 time-domain multiplexers 51 of the four post-processor modules 802 combines or integrates the corresponding set of the two-hundred-and-fifty signals Z₁-Z₂₅₀, each having a frequency bandwidth of J/250 sampled at a sampling rate of K/250, into a single corresponding signal or beam B₀ having a frequency bandwidth of J sampled at a sampling rate of K and outputs the corresponding signal or beam B₀ from its output. Each of the signals Z₁-Z₂₅₀ can be, but not limited to, sampled at least triple as fast as its bandwidth or maximum frequency. For example, if each of the signals Z₁-Z₂₅₀ has the bandwidth or maximum frequency of 2 MHz, each of the signals Z₁-Z₂₅₀ can be sampled at 6 Msps. Each of the four signals B₀ can be, but not limited to, sampled at least triple as fast as its bandwidth or maximum frequency. For example, if each of the four signals B₀ has the bandwidth or maximum frequency of 500 MHz, each of the four signals B₀ can be sampled at 1.5 Gsps.

Thereby, referring to FIGS. 3D, 3E and 3F, the broadband DBFN system 700 can process the thirty-two input signals A₀, each having a frequency bandwidth greater than that of each of the signals L₁-L₁₆ output from the preprocessor modules 800, greater than that of each of the signals M₁-M₁₆ input into the post-processor modules 802, and substantially equal to each signal B₀ output from the post-processor modules 802. The broadband DBFN system 700 can process the thirty-two input signals A₀ each sampled at a greater sampling rate than each of the signals L₁-L₁₆ output from the preprocessor modules 800 is sampled and than each of the signals M₁-M₁₆ input into the post-processor modules 802 is sampled. The broadband DBFN system 700 can process the thirty-two input signals A₀ each sampled at the same sampling rate as each signal B₀ output from the postprocessor modules 802 is sampled. Each of the signals A₀, X₁-X₂₅₆, Y₁-Y₂₅₆, L₁-L₁₆, M₁-M₁₆, W₁-W₂₅₆, S₁-S₂₅₆, Z₁-Z₂₅₆ and B₀ can be, but not limited to, sampled at least twice or triple its (maximum) frequency or bandwidth. All of the signals A₀ input to the thirty-two preprocessor modules 800 may have the same maximum frequency or bandwidth, and all of the signals A₀ input to the thirty-two preprocessor modules 800 may be sampled at the same sampling rate. Alternatively, the signals A₀ input to the thirty-two preprocessor modules 800 may have different maximum frequencies or bandwidths from one another, and the signals A₀ input to the thirty-two preprocessor modules 800 may be sampled at different sampling rates from one another.

Alternatively, the system 700 can include any number of narrowband DBFN modules 801, where the total number of the narrowband DBFN modules 801 is equal to any number greater than or equal to two, four, eight, sixteen, thirty two, or sixty four. Moreover, the system 700 can include any number of the preprocessor modules 800, where the total number of the preprocessor modules 800 is equal to any number greater than or equal to two, four, eight, sixteen, thirty two, or sixty four. The system 700 can include any number of the post-processor modules 802, where the total number of the post-processor modules 802 is equal to any number greater than or equal to two, four, eight, sixteen, thirty two, or sixty four.

Third Embodiment: Application to Linear Processor

Referring to FIG. 4A, a broad-band linear processing system 100 includes a preprocessing module or preprocessor 110, four narrowband (NB) linear processors 120 a, 120 b, 120 c and 120 d, and a post-processing module or post-processor 130. The preprocessor 100 can be, but not limited to, a single integrated circuit chip, a single system-on chip or a single chip package or implemented by using multiple integrated circuit chips, multiple system-on chips or multiple chip packages. The post-processor 130 can be, but not limited to, a single integrated circuit chip, a single system-on chip or a single chip package or implemented by using multiple integrated circuit chips, multiple system-on chips or multiple chip packages. The four linear processors 120 a, 120 b, 120 c and 120 d can be, but not limited to, embedded in a processing module or in the number Np of processing modules, where Np is an integer equal to or more than 2, 3 or 4. Each of the four linear processors 120 a, 120 b, 120 c and 120 d, for example, can be a multiplier, an adder, a subtractor or a divider. Alternatively, each of the four linear processors 120 a, 120 b, 120 c and 120 d may include, but not limited to, one or more multipliers, one or more adders, one or more subtractors, or/and one or more dividers. In the other words, each of the linear processors 120 a, 120 b, 120 c and 120 d can perform at least one of addition, subtraction, multiplication and division to its input signal. Each of the four linear processors 120 a, 120 b, 120 c and 120 d, for example, can be made of resistors, capacitors, inductors, transformers and so on without any transistor. All of the four linear processors 120 a, 120 b, 120 c and 120 d may have the same processing speed and capability or different processing speeds and capabilities.

Referring to FIG. 4A, the preprocessor 110 may include a 1-to-3 time-domain demultiplexer (TDDM) 50 and a wave-front multiplexer 213. The description of the 1-to-3 time-domain demultiplexer 50 illustrated in FIG. 4A can be referred to as the description of the 1-to-3 time-domain demultiplexer 50 as illustrated in FIG. 3A. The description of the wave-front multiplexer 213 illustrated in FIG. 4A can be referred to as the description of the wave-front multiplexer 213 as illustrated in FIG. 1A, 1B or 3A. The post-processor 130 may include a 3-to-1 time-domain multiplexer (TDM) 51, an equalizer 231, a wave-front demultiplexer 232, and an optimizer 235. The description of the 3-to-1 time-domain multiplexer 51 illustrated in FIG. 4A can be referred to as the description of the 3-to-1 time-domain multiplexer 51 as illustrated in FIG. 3A. The description of the wave-front demultiplexer 232 illustrated in FIG. 4A can be referred to as the description of the wave-front demultiplexer 232 as illustrated in FIG. 1A, 1B or 3A. The description of the equalizer 231 illustrated in FIG. 4A can be referred to as the description of the equalizer 231 as illustrated in FIG. 1B or 3A. The description of the optimizer 235 illustrated in FIG. 4A can be referred to as the description of the optimizer 235 as illustrated in FIG. 1B or 3A.

In FIG. 4A, the orthogonal functional transformation characterizing the wave-front multiplexer 213 can be, but not limited to, fast Fourier transformation (FFT), and the inverse orthogonal functional transformation characterizing the wave-front demultiplexer 232 can be, but not limited to, inverse fast Fourier transformation (IFFT). Alternatively, the orthogonal functional transformation characterizing the wave-front multiplexer 213 can be, but not limited to, Hadamard transformation, and the inverse orthogonal functional transformation characterizing the wave-front demultiplexer 232 can be, but not limited to, Hadamard transformation.

A method for processing signals or data streams by using the system 200 shown in FIG. 4A is described below. Referring to FIG. 4A, a signal A₁ is transmitted into the 1-to-3 time-domain demultiplexer 50 through, e.g., a signal path, a wireless channel or a physical channel, and the 1-to-3 time-domain demultiplexer 50 divides the received signal A₁, having a frequency bandwidth of J sampled at a sampling rate of K, into three signals X₁, X₂ and X₃, each having a frequency bandwidth of J/3 sampled at a sampling rate of K/3, output in parallel from its three outputs. Next, the three signals X₁, X₂ and X₃ and an pilot or diagnostic signal X₄ are respectively transmitted in parallel to four input ports 2 a, 2 b, 2 c and 2 d of the wave-front multiplexer 213. The pilot or diagnostic signal X₄ may have a single frequency and fixed amplitude. Alternatively, the pilot or diagnostic signal X₄ could change based on time or could be any signal known by the system 100. In contrast, the three signals X₁, X₂ and X₃ are unknown by the system 100. The signal A₁ input into the preprocessor module 110 is unknown by the system 100.

Referring to FIG. 4A, after the four signals X₁, X₂, X₃ and X₄ are input into the wave-front multiplexer 213, the wave-front multiplexer 213 performs the above-mentioned wave-front multiplexing transformation to process the signals X₁, X₂, X₃ and X₄ into four linear combinations, each combined with the four signals X₁, X₂, X₃ and X₄ multiplied by respective weightings, represented by four signals Y₁, Y₂, Y₃ and Y₄ each having a frequency bandwidth of J/3 sampled at a sampling rate of K/3. Next, the wave-front multiplexer 213 outputs the four signals Y₁, Y₂, Y₃ and Y₄ from its output ports 3 a, 3 b, 3 c and 3 d, and the signals Y₁, Y₂, Y₃ and Y₄ are transmitted to four input ports 14 a, 14 b, 14 c and 14 d of the four narrowband linear processors 120 a, 120 b, 120 c and 120 d through, e.g., four parallel signal paths, four parallel wireless channels or four parallel physical channels.

Referring to FIG. 4A, after the four signals Y₁, Y₂, Y₃ and Y₄ are input into the four narrowband linear processors 120 a, 120 b, 120 c and 120 d, the four narrowband linear processors 120 a, 120 b, 120 c and 120 d perform at least one of addition, subtraction, multiplication and division to the four respective signals Y₁, Y₂, Y₃ and Y₄ into four respective signals W₁, W₂, W₃ and W₄ each having a frequency bandwidth of J/3 sampled at a sampling rate of K/3 and outputs the four signals W₁, W₂, W₃ and W₄ from their output ports 15 a, 15 b, 15 c and 15 d. Next, the four signals W₁, W₂, W₃ and W₄ are transmitted in parallel to four input ports 10 a, 10 b, 10 c and 10 d of the equalizer 231 through, e.g., four parallel signal paths, four parallel wireless channels or four parallel physical channels. The input ports 10 a, 10 b, 10 c and 10 d are arranged in parallel for receiving the four signals W₁, W₂, W₃ and W₄, respectively. After the four signals W₁, W₂, W₃ and W₄ are transmitted in parallel into the equalizer 231, an optimizing and equalizing process is performed such that the four signals W₁, W₂, W₃ and W₄ can be compensated to be multiplied by four respective weightings by the equalizer 231, wherein the four respective weightings of the equalizer 231 can be adjusted based on a control signal CS output from the optimizer 235 and input into the equalizer 231. The optimizing and equalizing process can be referred to as the optimizing and equalizing process as illustrated in FIGS. 1B and 1C.

Referring to FIG. 4A, after the optimizing and equalizing process, the equalizer 231 outputs four equalized signals S₁, S₂, S₃ and S₄, each having a frequency bandwidth of J/3 sampled at a sampling rate of K/3, from its output ports 11 a, 11 b, 11 c and 11 d. The equalized signal S₁ is created by the equalizer 231 multiplying the signal W₁ by one of the weightings of the equalizer 231, the equalized signal S₂ is created by the equalizer 231 multiplying the signal W₂ by another one of the weightings of the equalizer 231, the equalized signal S₃ is created by the equalizer 231 multiplying the signal W₃ by another one of the weightings of the equalizer 231, and the equalized signal S₄ is created by the equalizer 231 multiplying the signal W₄ by the other one of the weightings of the equalizer 231. Each of the four respective weightings of the equalizer 231 can be, but not limited to, a complex value such that the equalized signals S₁, S₂, S₃ and S₄ can be rotated precisely to become in phase. In this case, the equalizer 231 can be performed by the narrow band equalizer, as illustrated in FIG. 1C. Alternatively, the equalizer 231 can be performed by the broadband equalizer, as illustrated in FIG. 1C.

Next, referring to FIG. 4A, the equalized signals S₁, S₂, S₃ and S₄ are transmitted in parallel to input ports 6 a, 6 b, 6 c and 6 d of the wave-front demultiplexer 232 through, e.g., four parallel signal paths or channels between the output ports 11 a, 11 b, 11 c and 11 d of the equalizer 231 and the input ports 6 a, 6 b, 6 c and 6 d of the wave-front demultiplexer 232.

Referring to FIG. 4A, after the equalized signals S₁, S₂, S₃ and S₄ are input in parallel to the wave-front demultiplexer 232, the wave-front demultiplexer 232 performs the above-mentioned wave-front demultiplexing transformation to process the equalized signals S₁, S₂, S₃ and S₄ into four linear combinations, each combined with the equalized signals S₁, S₂, S₃ and S₄ multiplied by respective weightings, represented by four signals Z₁, Z₂, Z₃ and Z₄, each having a frequency bandwidth of J/3 sampled at a sampling rate of K/3, output in parallel from its four parallel output ports 7 a, 7 b, 7 c and 7 d.

Next, referring to FIG. 4A, the three signals Z₁, Z₂ and Z₃ are transmitted in parallel to three input ports of the 3-to-1 time-domain multiplexer 51, and the signal Z₄ is transmitted into the optimizer 235. The signal Z₄ can be used as an output pilot or diagnostic signal featuring a value to be compared with that featured by the input pilot or diagnostic signal X₄ during the optimizing and equalizing process. After the three signals Z₁, Z₂ and Z₃ are input into the 3-to-1 time-domain multiplexer 51, the 3-to-1 time-domain multiplexer 51 combines or integrates the three signals Z₁, Z₂ and Z₃ into a single signal B₁ having a frequency bandwidth of J sampled at a sampling rate of K and outputs the signal B₁ from its output port.

Therefore, the broad-band linear processing system 100 illustrated in FIG. 4A can process the input signal A₁ having a bandwidth greater than that of each of the four signals Y₁, Y₂, Y₃ and Y₄ input into the four narrowband linear processors 120 a, 120 b, 120 c and 120 d, greater than that of each of the four signals W₁, W₂, W₃ and W₄ output from the four narrowband linear processors 120 a, 120 b, 120 c and 120 d, and substantially equal to that of the signal B₁ output from the 3-to-1 time-domain multiplexer 51. The signal A₁ may have a frequency, such as maximum frequency, or bandwidth substantially equal to that of the signal B₁ and at least three times higher than that of each of the signals X₁, X₂, X₃, X₄, Y₁, Y₂, Y₃, Y₄, W₁, W₂, W₃, W₄, S₁, S₂, S₃, S₄, Z₁, Z₂, Z₃ and Z₄.

Alternatively, referring to FIG. 4B, the 1-to-3 time-domain demultiplexer 50 of the system 100 illustrated in FIG. 4A can be replaced with the 1-to-M time-domain demultiplexer mentioned in the second embodiment, and the 3-to-1 time-domain multiplexer 51 of the system 100 illustrated in FIG. 4A can be replaced with the M-to-1 time-domain multiplexer mentioned in the second embodiment, where M is an integer equal to or greater than 4, 8, 16, 32, 64 or 256. In this case, the system 100 illustrated in FIG. 4B includes the number M+2 of (narrowband) linear processors 120. The wave-front multiplexer 213 of the system 200 illustrated in FIG. 4B processes the number M+2 of input signals X₁-X_(M+2) into the number M+2 of output signals Y₁-Y_(M+2). The equalizer 231 of the system 200 illustrated in FIG. 4B performs amplitude, phase, and time-delay compensation to adjust the amplitudes, phases, and/or time-delays of the number M+2 of signals W₁-W_(M+2) and outputs the number M+2 of the equalized signals S₁-S_(M+2). The wave-front demultiplexer 232 of the system 200 illustrated in FIG. 4B processes the number M+2 of the signals S₁-S_(M+2) into the number M+2 of output signals Z₁-Z_(M+2). The 1-to-M time-domain demultiplexer 50 of the system 100 illustrated in FIG. 4B divides a signal A₁ into the number M of the signals X₁-X_(M). The M-to-1 time-domain multiplexer 51 of the system 100 illustrated in FIG. 4B combines or integrates the number M of the signals Z₁-Z_(M) into an output signal B₁.

Referring to FIG. 4B, the linear processors 120 can be, but not limited to, embedded in a processing module or in the number Nm of processing modules, where Nm is an integer equal to or more than 2, 3, 4, 5, 6, 7 or 8. Each of the linear processors 120, for example, can be a multiplier, an adder, a subtractor or a divider. Alternatively, each of the linear processors 120 may include, but not limited to, one or more multipliers, one or more adders, one or more subtractors, or/and one or more dividers. All of the linear processors 120 may have the same processing speed and capability or different processing speeds and capabilities.

In FIG. 4B, the orthogonal functional transformation characterizing the wave-front multiplexer 213 can be, but not limited to, fast Fourier transformation (FFT), and the inverse orthogonal functional transformation characterizing the wave-front demultiplexer 232 can be, but not limited to, inverse fast Fourier transformation (IFFT). Alternatively, the orthogonal functional transformation characterizing the wave-front multiplexer 213 can be, but not limited to, Hadamard transformation, and the inverse orthogonal functional transformation characterizing the wave-front demultiplexer 232 can be, but not limited to, Hadamard transformation.

A method for processing signals or data streams by using the system 100 shown in FIG. 4B is described below. Referring to FIG. 4B, the signal A₁ is transmitted into the 1-to-M time-domain demultiplexer 50 through, e.g., a signal path, a wireless channel or a physical channel, and the 1-to-M time-domain demultiplexer 50 divides the signal A₁, having a frequency bandwidth of J sampled at a sampling rate of K, into the signals X₁-X_(M), each having a frequency bandwidth of J/M sampled at a sampling rate of K/M. Next, the signals X₁-X_(M) and two pilot or diagnostic signals X_(M+1) and X_(M+2) are respectively transmitted in parallel to the number M+2 of input ports of the wave-front multiplexer 213. Each of the pilot or diagnostic signals X_(M+1) and X_(M+2) may have a single frequency and fixed amplitude. Alternatively, each of the pilot or diagnostic signals X_(M+1) and X_(M+2) could change based on time or could be any signal known by the system 100. In contrast, the signals X₁-X_(M) are unknown by the system 100. The signal A₁ input into the preprocessor module 110 is unknown by the system 100.

Referring to FIG. 4B, after the signals X₁-X_(M+2) are input into the wave-front multiplexer 213, the wave-front multiplexer 213 performs the above-mentioned wave-front multiplexing transformation to process the signals X₁-X_(M+2) into the number M+2 of linear combinations, each combined with the signals X₁-X_(M+2) multiplied by respective weightings, represented by the signals Y₁-Y_(M+2) each having a frequency bandwidth of J/M sampled at a sampling rate of K/M. Next, the wave-front multiplexer 213 outputs the signals Y₁-Y_(M+2) from its output ports, and the signals Y₁-Y_(M+2) are respectively transmitted in parallel to the narrowband linear processors 120 through, e.g., multiple parallel signal paths, multiple parallel wireless channels or multiple parallel physical channels.

Referring to FIG. 4B, after the signals Y₁-Y_(M+2) are input into the narrowband linear processors 120, the narrowband linear processors 120 perform at least one of addition, subtraction, multiplication and division to the respective signals Y₁-Y_(M+2) into the respective signals W₁-W_(M+2) each having a frequency bandwidth of J/M sampled at a sampling rate of K/M and outputs the signals W₁-W_(M+2) from their output ports. Next, the signals W₁-W_(M+2) are transmitted in parallel to the equalizer 231 through, e.g., multiple parallel signal paths, multiple parallel wireless channels or multiple parallel physical channels. Next, an optimizing and equalizing process is performed such that the signals W₁-W_(M+2) can be compensated to be multiplied by respective weightings by the equalizer 231, wherein the respective weightings of the equalizer 231 can be adjusted based on a control signal CS output from the optimizer 235 and input into the equalizer 231. The optimizing and equalizing process can be referred to as the optimizing and equalizing process as illustrated in FIG. 1C. After the optimizing and equalizing process, the equalizer 231 outputs the equalized signals S₁-S_(M+2), each having a frequency bandwidth of J/M sampled at a sampling rate of K/M, from its output ports. Each of the equalized signals S₁-S_(M+2) is created by the equalizer 231 multiplying the corresponding one of the signals W₁-W_(M+2) by a weighting of the equalizer 231. Each of the respective weightings of the equalizer 231 can be, but not limited to, a complex value such that the equalized signals S₁-S_(M+2) can be rotated precisely to become in phase. In this case, the equalizer 231 can be performed by the narrow band equalizer, as illustrated in FIG. 1C. Alternatively, the equalizer 231 can be performed by the broadband equalizer, as illustrated in FIG. 1C.

Next, referring to FIG. 4B, the equalized signals S₁-S_(M+2) are transmitted in parallel to the wave-front demultiplexer 232 through, e.g., multiple parallel signal paths, multiple wireless channels or multiple physical channels. Next, the wave-front demultiplexer 232 performs the above-mentioned wave-front demultiplexing transformation to process the equalized signals S₁-S_(M+2) into the number M of linear combinations, each combined with the equalized signals S₁-S_(M+2) multiplied by respective weightings, represented by the signals Z₁-Z_(M+2), each having a frequency bandwidth of J/M sampled at a sampling rate of K/M, output in parallel from its output ports.

Next, referring to FIG. 4B, the signals Z₁-Z_(M) are transmitted in parallel to the M-to-1 time-domain multiplexer 51, and the two signals Z_(M+1) and Z_(M+2) are transmitted into the optimizer 235. The signal Z_(M+1) is used as a first output pilot or diagnostic signal featuring a value to be compared with that featured by the input pilot or diagnostic signal X_(M+1) during the optimizing and equalizing process. The signal Z_(M+2) is used as a second output pilot or diagnostic signal featuring a value to be compared with that featured by the input pilot or diagnostic signal X_(M+2) during the optimizing and equalizing process. After the signals Z₁-Z_(M) are input into the M-to-1 time-domain multiplexer 51, the M-to-1 time-domain multiplexer 51 combines or integrates the signals Z₁-Z_(M) into the output signal B₁ having a frequency bandwidth of J sampled at a sampling rate of K and outputs the signal B₁ from its output port.

Therefore, the broad-band linear processing system 100 illustrated in FIG. 4B can process the input signal A₁ having a bandwidth greater than that of each of the signals Y₁-Y_(M+2) input into the narrowband linear processors 120, greater than that of each of the signals W₁-W_(M+2) output from the narrowband linear processors 120, and substantially equal to that of the signal B₁ output from the M-to-1 time-domain multiplexer 51. The signal A₁ may have a frequency, such as maximum frequency, or bandwidth substantially equal to that of the signal B₁ and at least M times higher than that of each of the signals X₁-X_(M+2), Y₁-Y_(M+2), W₁-W_(M+2), S₁-S_(M+2), and Z₁-Z_(M+2), where M is an integer equal to or greater than 4, 8, 16, 32, 64 or 256.

Referring to FIG. 4C, the preprocessor module 800 illustrated in FIG. 3E and the post-processor module 802 illustrated in FIG. 3F can be applied to a broad-band linear processing system 100. In this case, the system 100 shown in FIG. 4C includes sixteen (narrowband) linear processors 120 to process the sixteen signals L₁-L₁₆, output from the sixteen 16-to-1 time-domain multiplexers 52 a-52 p of the preprocessor module 800, into the sixteen signals M₁-M₁₆ and then output the sixteen signals M₁-M₁₆ to the sixteen 1-to-16 time-domain demultiplexers 53 a-53 p of the post-processor module 802. Thereby, the system 100 can process an input signal A₀ into an output signal B₀. All of the sixteen linear processors 120 shown in FIG. 4C, for example, may have the same processing speed and capability, and the sixteen 16-to-1 time-domain multiplexers 52 a-52 p of the preprocessor module 800 are identical. In FIG. 4C, the orthogonal functional transformation characterizing the wave-front multiplexer 213 can be, but not limited to, fast Fourier transformation (FFT), and the inverse orthogonal functional transformation characterizing the wave-front demultiplexer 232 can be, but not limited to, inverse fast Fourier transformation (IFFT).

A method for processing signals or data streams by using the system 100 shown in FIG. 4C is described below. Referring to FIG. 4C, the input signal A₀ is transmitted into the 1-to-250 time-domain demultiplexer 50 of the preprocessor module 800. Next, the 1-to-250 time-domain demultiplexer 50 divides the received signal A₀ having a frequency bandwidth of J sampled at a sampling rate of K into two-hundred-and-fifty signals X₁-X₂₅₀ each having a frequency bandwidth of J/250 sampled at a sampling rate of K/250 and outputs the two-hundred-and-fifty signals X₁-X₂₅₀ from its two-hundred-and-fifty outputs. The signals X₃-X₂₄₉ are not shown in FIG. 4C. Next, the two-hundred-and-fifty signals X₁-X₂₅₀ and six pilot or diagnostic signals X₂₅₁-X₂₅₆ are transmitted in parallel to the wave-front multiplexer 213. Each of the signals X₂₅₁₋₂₅₆ may have a single frequency and fixed amplitude. Alternatively, each of the signals X₂₅₁₋₂₅₆ could change based on time or could be any signal known by the system 100. In contrast, the two-hundred-and-fifty signals X₁-X₂₅₀ are unknown by the system 100. The signal A₀ is unknown by the system 100. The signal A₀ can be, but not limited to, sampled at least triple as fast as its bandwidth or maximum frequency. For example, if the signal A₀ has the bandwidth or maximum frequency of 500 MHz, the signal A₀ can be sampled at 1.5 Gsps.

Referring to FIG. 4C, after the two-hundred-and-fifty-six signals X₁-X₂₅₆ are input into the wave-front multiplexer 213, the wave-front multiplexer 213 performs the above-mentioned wave-front multiplexing transformation to process the signals X₁-X₂₅₆ into two-hundred-and-fifty-six linear combinations, each combined with the signals X₁-X₂₅₆ multiplied by respective weightings, represented by two-hundred-and-fifty-six signals Y₁-Y₂₅₆ and outputs the two-hundred-and-fifty-six signals Y₁-Y₂₅₆. Each of the signals Y₁-Y₂₅₆ may have a bandwidth of J/250 sampled at a sampling rate of K/250. The signals Y₂-Y₁₅, Y₁₈-Y₃₁, Y₃₃-Y₂₄₀, and Y₂₄₂-Y₂₅₅ are not shown in FIG. 4C. Next, sixteen sets of sixteen ones of the signals Y₁-Y₂₅₆ are respectively transmitted to the sixteen 16-to-1 time-domain multiplexers 52 a-52 p through, e.g., multiple parallel signal paths, multiple parallel physical channels or multiple parallel wireless channels. Each of the signals X₁-X₂₅₀ can be, but not limited to, sampled at least triple as fast as its bandwidth or maximum frequency. For example, if each of the signals X₁-X₂₅₀ has the bandwidth or maximum frequency of 2 MHz, each of the signals X₁-X₂₅₀ can be sampled at 6 Msps. Each of the signals Y₁-Y₂₅₀ can be, but not limited to, sampled at least triple as fast as its bandwidth or maximum frequency. For example, if each of the signals Y₁-Y₂₅₀ has the bandwidth or maximum frequency of 2 MHz, each of the signals Y₁-Y₂₅₀ can be sampled at 6 Msps.

Next, referring to FIG. 4C, each of the sixteen 16-to-1 time-domain multiplexers 52 a-52 p combines or integrates a corresponding set of the received sixteen ones of the signals Y₁-Y₂₅₆ into a corresponding one of the sixteen signals L₁-L₁₆ and outputs the corresponding one of the sixteen signals L₁-L₁₆ to a corresponding one of the sixteen linear processors 120. Each of the signals L₁-L₁₆ may have a bandwidth of 16*J/250 sampled at a sampling rate of 16*K/250. Only three linear processors 120 are shown in FIG. 4C, and only the three signals L₁, L₂ and L₁₆ are shown in FIG. 4C. Thereby, the sixteen signals L₁-L₁₆ output from the sixteen 16-to-1 time-domain multiplexers 52 a-52 p of the preprocessor module 800 are respectively transmitted in parallel to the sixteen linear processors 120. Each of the signals L₁-L₁₆ can be, but not limited to, sampled at least triple as fast as its bandwidth or maximum frequency. For example, if each of the signals L₁-L₁₆ has the bandwidth or maximum frequency of 32 MHz, each of the signals L₁-L₁₆ can be sampled at 96 Msps.

Next, referring to FIG. 4C, the sixteen linear processors 120 perform at least one of addition, subtraction, multiplication and division to the respective sixteen signals L₁-L₁₆ into the respective sixteen signals M₁-M₁₆ and output the signals M₁-M₁₆ to the sixteen 1-to-16 time-domain demultiplexers 53 a-53 p of the post-processor module 802. Each of the signals M₁-M₁₆ may have a bandwidth of 16*J/250 sampled at a sampling rate of 16*K/250. Each of the signals M₁-M₁₆ can be, but not limited to, sampled at least triple as fast as its bandwidth or maximum frequency. For example, if each of the signals M₁-M₁₆ has the bandwidth or maximum frequency of 32 MHz, each of the signals M₁-M₁₆ can be sampled at 96 Msps.

Next, referring to FIG. 4C, the sixteen 1-to-16 time-domain demultiplexers 53 a-53 p of the post-processor module 802 divide the received sixteen signals M₁-M₁₆ into two-hundred-and-fifty-six signals W₁-W₂₅₆ each having a frequency bandwidth of J/250 sampled at a sampling rate of K/250 and output the signals W₁-W₂₅₆ to the equalizer 231. Each of the sixteen 1-to-16 time-domain demultiplexers 53 a-53 p outputs sixteen corresponding ones of the signals W₁-W₂₅₆. For example, the 1-to-16 time-domain demultiplexer 53 a divides the received signal M₁, having a frequency bandwidth of 16*J/250 sampled at a sampling rate of 16*K/250, into the sixteen output signals W₁-W₁₆, each having a frequency bandwidth of J/250 sampled at a sampling rate of K/250, and outputs the sixteen output signals W₁-W₁₆ to the equalizer 231. The 1-to-16 time-domain demultiplexer 53 b divides the received signal M₂, having a frequency bandwidth of 16*J/250 sampled at a sampling rate of 16*K/250, into the sixteen output signals W₁₇-W₃₂, each having a frequency bandwidth of J/250 sampled at a sampling rate of K/250, and outputs the sixteen output signals W₁₇-W₃₂ to the equalizer 231. The 1-to-16 time-domain demultiplexer 53 p divides the received signal M₁₆, having a frequency bandwidth of 16*J/250 sampled at a sampling rate of 16*K/250, into the sixteen output signals W₂₄₁-W₂₅₆, each having a frequency bandwidth of J/250 sampled at a sampling rate of K/250, and outputs the sixteen output signals W₂₄₁-W₂₅₆ to the equalizer 231.

Next, referring to FIG. 4C, the post-processor module 802 may perform an optimizing and equalizing process by its equalizer 231 and its optimizer 235 to adjust the amplitudes, phases, and/or time-delays of the signals W₁-W₂₅₆ output from its sixteen 1-to-16 time-domain demultiplexers 53 a-53 p, and the equalizer 231 generates two-hundred-and-fifty-six equalized signals S₁-S₂₅₆ each having a frequency bandwidth of J/250 sampled at a sampling rate of K/250 and outputs the equalized signals S₁-S₂₅₆ to the wave-front demultiplexer 232. Each of the equalized signals S₁-S₂₅₆ is created by the equalizer 231 multiplying the corresponding one of the signals W₁-W₂₅₆ by a weighting of the equalizer 231. For example, the equalized signal S₁ is created by the equalizer 231 multiplying the corresponding signal W₁ by a weighting of the equalizer 231. The signals S₃-S₂₅₅ are not shown in FIG. 4C. Each of the signals W₁-W₂₅₆ can be, but not limited to, sampled at least triple as fast as its bandwidth or maximum frequency. For example, if each of the signals W₁-W₂₅₆ has the bandwidth or maximum frequency of 2 MHz, each of the signals W₁-W₂₅₆ can be sampled at 6 Msps. Each of the signals S₁-S₂₅₆ can be, but not limited to, sampled at least triple as fast as its bandwidth or maximum frequency. For example, if each of the signals S₁-S₂₅₆ has the bandwidth or maximum frequency of 2 MHz, each of the signals S₁-S₂₅₆ can be sampled at 6 Msps.

Next, referring to FIG. 4C, the wave-front demultiplexer 232 performs the above-mentioned wave-front demultiplexing transformation to process the equalized signals S₁-S₂₅₆ into two-hundred-and-fifty-six linear combinations, each combined with the signals S₁-S₂₅₆ multiplied by respective weightings, represented by two-hundred-and-fifty-six signals Z₁-Z₂₅₆ each having a frequency bandwidth of J/250 sampled at a sampling rate of K/250. Next, the wave-front demultiplexer 232 outputs the two-hundred-and-fifty signals Z₁-Z₂₅₀ to the 250-to-1 time-domain multiplexer 51 and outputs the six signals Z₂₅₁-Z₂₅₆ to the optimizer 235. The optimizer 235 generates a control signal CS and outputs the control signal CS to the equalizer 231 to adjust the weightings of the equalizer 231, as illustrated in FIG. 1C.

Referring to FIG. 4C, after the signals Z₁-Z₂₅₀ are input into the 250-to-1 time-domain multiplexer 51, the 250-to-1 time-domain multiplexer 51 combines or integrates the signals Z₁-Z₂₅₀, each having a frequency bandwidth of J/250 sampled at a sampling rate of K/250, into the signal B₀ having a frequency bandwidth of J sampled at a sampling rate of K and outputs the signal B₀ from its output. Each of the signals Z₁-Z₂₅₀ can be, but not limited to, sampled at least triple as fast as its bandwidth or maximum frequency. For example, if each of the signals Z₁-Z₂₅₀ has the bandwidth or maximum frequency of 2 MHz, each of the signals Z₁-Z₂₅₀ can be sampled at 6 Msps. The signal B₀ can be, but not limited to, sampled at least triple as fast as its bandwidth or maximum frequency. For example, the signal B₀ has the bandwidth or maximum frequency of 500 MHz, the signal B₀ can be sampled at 1.5 Gsps.

Thereby, referring to FIG. 4C, the system 100 can process the signal A₀, having a frequency bandwidth greater than that of each of the signals L₁-L₁₆, greater than that of each of the signals M₁-M₁₆, and substantially equal to the signal B₀. The system 100 can process the signal A₀ sampled at a greater sampling rate than each of the signals L₁-L₁₆ is sampled and than each of the signals M₁-M₁₆ is sampled. The system 100 can process the signal A₀ sampled at the same sampling rate as the signal B₀ is sampled.

Alternatively, the sixteen 16-to-1 time-domain multiplexers 52 a-52 p of the preprocessor module 800 shown in FIG. 4C can be replaced with sixteen frequency division or domain multiplexers (FDMs), and the sixteen 1-to-16 time-domain demultiplexers 53 a-53 p of the post-processor module 802 can be replaced with sixteen frequency division or domain demultiplexers.

The linear processors can operate at different processing speeds and capabilities, and thereby the multiplexer 213 and demultiplexer 232 can allocate the different number of I/O ports for different linear processors 120 based on their processing speeds and capabilities. For example, in FIG. 4B, both multiplexers and demultiplexers can provide the number N_(L) of sets of one port for the number N_(L) of the linear processors, respectively and provide the number N_(V) of sets of multiple ports for the number N_(V) of the linear processors, respectively. Each of the number N_(V) of the linear processors operates at higher processing speeds and capabilities than each of the number N_(L) of the linear processors operates. In this case, the number N_(L)+N_(V) can be less than the total number M+2 of output ports of the wave-front multiplexer 213 and less than the total number M+2 of input ports of the wave-front demultiplexer 213. Alternatively, in FIG. 4C, the number N_(B) of linear processors 120 each receive one signal from a corresponding 16-to-1 time domain multiplexer and output one signal to a corresponding 1-to-16 time domain demultiplexer, and the number N_(C) of linear processors 120 each receive multiple signals from multiple corresponding 16-to-1 time domain multiplexers and output multiple signals to multiple corresponding 1-to-16 time domain demultiplexers. Each of the number N_(C) of the linear processors operates at higher processing speeds and capabilities than each of the number N_(B) of the linear processors operates. In this case, the number N_(B)+N_(C) can be less than the total number of the 16-to-1 time domain multiplexers and less than the total number of input ports of the 1-to-16 time domain demultiplexers.

Alternatively, the sixteen 16-to-1 time-domain multiplexers 52 a-52 p of the preprocessor module 800 shown in FIG. 4C can be replaced with sixteen code division or domain multiplexers (CDMs), and the sixteen 1-to-16 time-domain demultiplexers 53 a-53 p of the post-processor module 802 can be replaced with sixteen code division or domain demultiplexers. In this case, the sixteen linear processors 120 shown in FIG. 4C can operate at different processing speeds and capabilities.

FIG. 4D shows that two signals or data streams A₀ and A₁ are processed by a linear processing system 100 so as to output two signals or data streams B₀ and B₁. Referring to FIG. 4D, the preprocessor module 800 shown in FIG. 4D is similar to the preprocessor module 800 illustrated in FIG. 4C except that the preprocessor module 800 shown in FIG. 4D includes two 1-to-M time-domain demultiplexers, such as 1-to-150 time-domain demultiplexer 50 a and 1-to-100 time-domain demultiplexer 50 b, processing the two input signals or data streams A₀ and A₁ into two-hundred-and-fifty signals or data streams X₁-X₂₅₀. The post-processor module 802 shown in FIG. 4D is similar to the post-processor module 802 illustrated in FIG. 4C except that the post-processor module 802 shown in FIG. 4D includes two M-to-1 time-domain multiplexers, such as 150-to-1 time-domain multiplexer 51 a and 100-to-1 time-domain multiplexer 51 b, processing two-hundred-and-fifty signals or data streams Z₁-Z₂₅₀ into output the two signals or data streams B₀ and B₁.

A method for processing signals or data streams by using the system 100 shown in FIG. 4D is briefly described below. Referring to FIG. 4D, the input signal A₀ is transmitted into the 1-to-150 time-domain demultiplexer 50 a of the preprocessor module 800, and the input signal A₁ is transmitted into the 1-to-100 time-domain demultiplexer 50 b of the preprocessor module 800. Next, the 1-to-150 time-domain demultiplexer 50 a divides the received signal A₀ into one-hundred-and-fifty signals X₁-X₁₅₀ and outputs the signals X₁-X₁₅₀ from its output ports, and the 1-to-100 time-domain demultiplexer 50 b divides the received signal A₁ into one-hundred signals X₁₅₁-X₂₅₀ and outputs the signals X₁₅₁-X₂₅₀ from its output ports. Next, the two-hundred-and-fifty signals X₁-X₂₅₀ and six pilot or diagnostic signals X₂₅₁-X₂₅₆ are transmitted in parallel to the wave-front multiplexer 213. Each of the signals X₂₅₁₋₂₅₆ may have a single frequency and fixed amplitude. Alternatively, each of the signals X₂₅₁₋₂₅₆ could change based on time or could be any signal known by the system 100. In contrast, the two-hundred-and-fifty signals X₁-X₂₅₀ are unknown by the system 100. The signals A₀ and A₁ are unknown by the system 100. Next, the following processing steps can be referred to as the corresponding processing steps as illustrated in FIG. 4C so as to generate two-hundred-and-fifty-six signals Z₁-Z₂₅₆. Next, the one-hundred-and-fifty signals Z₁-Z₁₅₀ are transmitted in parallel to the 150-to-1 time-domain multiplexer 51 a, the one-hundred signals Z₁₅₁-Z₂₅₀ are transmitted in parallel to the 100-to-1 time-domain multiplexer 51 b, and the six signals Z₂₅₁-Z₂₅₆ are transmitted to the optimizer 235. The optimizer 235 generates a control signal CS and outputs the control signal CS to the equalizer 231 to adjust the weightings of the equalizer 231, as illustrated in FIG. 1C.

Referring to FIG. 4D, after the signals Z₁-Z₁₅₀ are input into the 150-to-1 time-domain multiplexer 51 a, the 150-to-1 time-domain multiplexer 51 a combines or integrates the signals Z₁-Z₁₅₀ into the signal B₀ and outputs the signal B₀ from its output. After the signals Z₁₅₁-Z₂₅₀ are input into the 100-to-1 time-domain multiplexer 51 b, the 100-to-1 time-domain multiplexer 51 b combines or integrates the signals Z₁₅₁-Z₂₅₀ into the signal B₁ and outputs the signal B₁ from its output.

Thereby, referring to FIG. 4D, the system 100 processes the signal A₀, having a frequency bandwidth greater than that of each of the signals L₁-L₁₆, greater than that of each of the signals M₁-M₁₆, and substantially equal to the signal B₀ and processes the signal A₁, having a frequency bandwidth greater than that of each of the signals L₁-L₁₆, greater than that of each of the signals M₁-M₁₆, and substantially equal to the signal B₁. The system 100 processes the signals A₀ and A₁ each sampled at a greater sampling rate than each of the signals L₁-L₁₆ is sampled and than each of the signals M₁-M₁₆ is sampled. The system 100 processes the signal A₀ sampled at substantially the same sampling rate as the signal B₀ is sampled and processes the signal A₁ sampled at substantially the same sampling rate as the signal B₁ is sampled. Each of the signals A₀, X₁-X₂₅₆, Y₁-Y₂₅₆, L₁-L₁₆, M₁-M₁₆, W₁-W₂₅₆, S₁-S₂₅₆, Z₁-Z₂₅₆ and B₀ can be, but not limited to, sampled at least twice or triple its (maximum) frequency or bandwidth.

Referring to FIG. 4E, the system 100 shown in FIG. 4E is similar to the system 100 illustrated in FIG. 4A except that the preprocessor 110 shown in FIG. 4E does not include the 1-to-3 time-domain demultiplexer 50 and that the post-processor 130 shown in FIG. 4E does not include the 3-to-1 time-domain multiplexer 51.

A method for processing signals or data streams by using the system 200 shown in FIG. 4E is briefly described below. Three signals X₁, X₂ and X₃ and a pilot or diagnostic signal X₄ are transmitted in parallel to the wave-front multiplexer 213. Next, the following processing steps can be referred to as the corresponding processing steps as illustrated in FIG. 4A so as to generate four signals Z₁-Z₄.

FIG. 4F shows a numerical example of the system 100 illustrated in FIG. 4E using Hadamard transformations performed by the wave-front multiplexer 213 and the wave-front demultiplexer 232. In this case, the four linear processors 120 a, 120 b, 120 c and 120 d feature multiplication by a scalar, and each of the four linear processors 120 a, 120 b, 120 c and 120 d has a sampling rate of 1 Msps. The descriptions of the wave-front multiplexer 213 and the wave-front demultiplexer 232 as illustrated in FIG. 1A can be applied to this embodiment illustrated in FIGS. 4E and 4F.

Referring to FIGS. 4E and 4F, the number of −6 represents a slice, i.e. slice a, of the input signal X₁, the number of −4 represents a slice, i.e. slice b, of the input signal X₂, the number of −1 represents a slice, i.e. slice c, of the input signal X₃, and the pilot code of i represents a slice, i.e. slice d, of the pilot or diagnostic signal X₄. After the four slices a, b, c and d are input into the wave-front multiplexer 213, the wave-front multiplexer 213 performs the wave-front multiplexing transform, which can be referred to as the description illustrated in FIG. 1A. In this case, the system 100 uses the same 4*4 Hadamard matrixes Ba and Ea to achieve the wave-front multiplexing and demultiplexing transforms, respectively. An input matrix Aa including the four slices a, b, c and d shown in FIG. 4F can represent the input matrix A illustrated in FIG. 1A. A 4×4 Hadamard matrix Ba shown in FIG. 4F can represent the orthogonal matrix B illustrated in FIG. 1A. The first column of the matrix Ba is defined herein as a first wave-front multiplexing vector (WFMV1) for processing the slice a. The second column of the matrix Ba is defined herein as a second wave-front multiplexing vector (WFMV2) for processing the slice b. The third column of the matrix Ba is defined herein as a third wave-front multiplexing vector (WFMV3) for processing the slice c. The fourth column of the matrix Ba is defined herein as a fourth wave-front multiplexing vector (WFMV4) for processing the slice d.

After performing the wave-front multiplexing transform, the wave-front multiplexer 213 obtains four output signals Y₁, Y₂, Y₃ and Y₄ represented by a 4×1 matrix Ca, which can represent the matrix C illustrated in FIG. 1A, and then outputs the four output signals Y₁, Y₂, Y₃ and Y₄ from its four outputs 3 a, 3 b, 3 c and 3 d. Next, the four output signals Y₁, Y₂, Y₃ and Y₄ are respectively transmitted in parallel to four input ports 14 a, 14 b, 14 c and 14 d of the four linear processors 120 a, 120 b, 120 c and 120 d through, e.g., four parallel signal paths, four parallel wireless channels or four parallel physical channels. Next, each of the four linear processors 120 a, 120 b, 120 c and 120 d processes a corresponding one of the four signals Y₁, Y₂, Y₃ and Y₄ to be multiplied by a constant of 3 at a sampling rate of 1 Msps. Next, the four linear processors 120 a, 120 b, 120 c and 120 d respectively output four signals W₁, W₂, W₃ and W₄ to four input ports 10 a, 10 b, 10 c and 10 d of the equalizer 231 through, e.g., four parallel signal paths, four parallel wireless channels or four parallel physical channels. After the four signals W₁, W₂, W₃ and W₄ are transmitted in parallel into the equalizer 231, an optimizing and equalizing process is performed such that the four signals W₁, W₂, W₃ and W₄ can be compensated to be multiplied by four respective weightings by the equalizer 231, wherein the four respective weightings of the equalizer 231 can be adjusted based on a control signal CS output from the optimizer 235 and input into the equalizer 231. The optimizing and equalizing process can be referred to as the optimizing and equalizing process as illustrated in FIGS. 1B and 1C.

After the optimizing and equalizing process, the equalizer 231 outputs four equalized signals S₁, S₂, S₃ and S₄ represented by a 4×1 matrix Da, which can represent the matrix D illustrated in FIG. 1A, from its output ports 11 a, 11 b, 11 c and 11 d. Next, the four signals S₁, S₂, S₃ and S₄ are transmitted in parallel to input ports 6 a, 6 b, 6 c and 6 d of the wave-front demultiplexer 232 through, e.g., four parallel signal paths or channels between the output ports 11 a, 11 b, 11 c and 11 d of the equalizer 231 and the input ports 6 a, 6 b, 6 c and 6 d of the wave-front demultiplexer 232. After the equalized signals S₁, S₂, S₃ and S₄ are input in parallel to the wave-front demultiplexer 232, the wave-front demultiplexer 232 performs the wave-front demultiplexing transform, which can be referred to as the description illustrated in FIG. 1A. A 4×4 Hadamard matrix Ea shown in FIG. 4F can represent the orthogonal matrix E illustrated in FIG. 1A. The first column of the matrix Ea is defined herein as a first wave-front demultiplexing vector (WFDV1) for processing the component of (−33/2+i3/2) in the matrix Da. The second column of the matrix Ea is defined herein as a second wave-front demultiplexing vector (WFDV2) for processing the component of (−27/2+i3/2) in the matrix Da. The third column of the matrix Ea is defined herein as a third wave-front demultiplexing vector (WFDV3) for processing the component of (−9/2+i3/2) in the matrix Da. The fourth column of the matrix Ea is defined herein as a fourth wave-front demultiplexing vector (WFDV4) for processing the component of (−3/2+i3/2) in the matrix Da.

After performing the wave-front demultiplexing transform, the wave-front demultiplexer 232 obtains four signals Z₁, Z₂, Z₃ and Z₄ represented by a 4×1 matrix Fa, which can represent the matrix F illustrated in FIG. 1A, and outputs the four signals Z₁, Z₂, Z₃ and Z₄. The signal Z₄ is transmitted into the optimizer 235. The signal Z₄ can be used as an output pilot or diagnostic signal featuring a value to be compared with that featured by the input pilot or diagnostic signal X₄ during the optimizing and equalizing process.

FIG. 4F also shows a broad-band linear processor 60, which is not part of the system 100, to process the three slices a, b and c multiplied by a constant of 3 at a sampling rate of 3 Msps. In contrast, the system 100 can use four narrowband linear processors 120 a, 120 b, 120 c and 120 d to achieve the same purpose that the broad-band linear processor 60 achieved.

Fourth Embodiment: Application to Fiber Optical Communications

FIGS. 5A and 5C-5H show multiple systems each including fiber optical communication using multiple light sources and various propagation paths grouped with a wave-front multiplexer and a wave-front demultiplexer according to an exemplary embodiment of the present disclosure. These systems in accordance with the fourth embodiment create various mode groups (MGs) of light via mode group diversity multiplexing (MGDM) as means for multiple parallel paths in a multimode fiber (MMF). Alternatively, instead of the mode group diversity multiplexing, the systems in accordance with the embodiment could perform a wavelength diversity multiplexing (WDM) process to create multiple wavelengths, i.e. various colorful lasers or light beams, passing through multiple single mode fibers.

Referring to FIG. 5A, a system 500 includes a wave-front multiplexer 213, four individual optical transmit devices or transmitters 520 a, 520 b, 520 c and 520 d, four individual optical detectors 522 a, 522 b, 522 c and 522 d, a mode group diversity multiplexing (MGDM) device 516, a mode group diversity demultiplexing (MGDDM) device 518, a multimode fiber (MMF) 524, an equalizer or equalization processor 231, a wave-front demultiplexer 232, and an optimizer or optimization processor 235. The description of the wave-front multiplexer 213 illustrated in FIG. 5A can be referred to as that as illustrated in FIG. 1A or 1B. The description of the wave-front demultiplexer 232 illustrated in FIG. 5A can be referred to as that as illustrated in FIG. 1A or 1B. The description of the equalizer 231 illustrated in FIG. 5A can be referred to as that as illustrated in FIG. 1B. The description of the optimizer 235 illustrated in FIG. 5A can be referred to as that as illustrated in FIG. 1B.

Each of the optical transmit devices 520 a, 520 b, 520 c and 520 d includes a laser generator or light source, e.g., including one or more light-emitting-diode (LED) chips, wherein the optical transmit devices 520 a, 520 b, 520 c and 520 d can be, but not limited to, integrated or embedded in hardware such as module or processor. In this embodiment, the processor 998 including the four processing units 999 a, 999 b, 999 c and 999 d as illustrated in FIG. 1A can be replaced with a communication medium including the four optical transmit devices 520 a-520 d, the four optical detectors 522 a-522 d and the MMF 524 as illustrated in FIG. 5A.

The MMF 524 provides multiple concurrent pairs of optical transmit devices 520 a-520 d and detectors 522 a-522 d over an optical carrier frequency (or optical wavelength) with good isolations among the pairs via multiple mode-group (MG) diversity in the MMF 524 in optical communications to increase the communication capacity of the MMF 524. In the MMF 524, various signals in different propagation mode-groups (MGs) feature “mutual coupling” at the same frequency or wavelength due to imperfections of the optical fiber, e.g. non perfect circular cross-sections, temperature gradient, inhomogeneous densities, mechanical bending of fibers, and etc., as illustrated in FIG. 5B depicting a mathematical model of mode-coupling among four propagation paths in the MMF 524. In the current multimode fiber, normalized power radiated by an optical transmit devices would be scattered into multiple portions captured by different optical detectors. For example, referring to FIG. 5B, some of the coupling coefficients C₁₁, C₂₂, C₃₃, C₄₄, C₂₁, C₁₂, C₂₃, C₃₂, C₃₄ and C₄₃ among the four propagation paths from various sources, such as optical transmit devices 520 a, 520 b, 520 c and 520 d, to different destinations, such as optical detectors 522 a, 522 b, 522 c and 522 d are illustrated. C₁₁ is the coupling coefficient between the optical transmits device 520 a and the optical detector 522 a and standing for amount of power captured by the optical detector 522 a from a normalized power radiated by the optical transmit device 520 a. C₁₂ is the coupling coefficient between the optical transmits device 520 a and optical detector 522 b and standing for amount of power captured by the optical detector 522 b from a normalized power radiated by the optical transmit device 520 a. C₂₃ is the coupling coefficient between the optical transmits device 520 b and optical detector 522 c and standing for amount of power captured by the optical detector 522 c from a normalized power radiated by the optical transmit device 520 b. As a result, signals radiated by the optical transmit device 520 a might not only appear at the optical detector 522 a but also at the optical detectors 522 b, 522 c and 522 d.

Referring to FIG. 5A, the wave-front multiplexer 213 can receive, in parallel, four individual and independent digital signals X₁, X₂, X₃ and X₄, to process the digital signals X₁, X₂, X₃ and X₄ into four digital signals Y₁, Y₂, Y₃ and Y₄ by the above-mentioned wave-front multiplexing transform, and outputs the digital signals Y₁, Y₂, Y₃ and Y₄ in parallel, which can be referred to as the description illustrated in FIG. 1A. Each of the digital signals Y₁, Y₂, Y₃ and Y₄ is a linear combination, i.e. weighted sum, each combined with the digital signals X₁, X₂, X₃ and X₄ multiplied by respective weightings, and distributions of the weightings of any two input components in all digital signals Y₁, Y₂, Y₃ and Y₄ are orthogonal, which can be referred to as the description illustrated in FIGS. 1A and 1D. In this case, as illustrated in FIG. 1D, the number of H is equal to 4. The wave-front multiplexer 213 has 4*4 computing units and four summing processors. The computing units form a processor array with four rows and four columns. The input signals X₁-X₄ can be received by the computing units in the respective four columns in the processor array. Upon receiving the input signals X₁-X₄, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The four summing processors can output the four signals Y₁-Y₄ each combined with the weighted signals output from the computing units in a corresponding one of the four rows in the processor array. The digital signals X₁, X₂, X₃ and X₄ can be, but not limited to, four IF digital signals or four RF digital signals.

The signal X₄ may be a pilot or diagnostic signal that may have a single frequency and fixed amplitude. Alternatively, the pilot or diagnostic signal X₄ could change based on time or could be any signal known by the system 500. The extraneous signals X₁, X₂ and X₃ are unknown by the system 500 and input into the system 500 from an extraneous system.

The wave-front multiplexer 213 can be, but not limited to, embedded in a processor. The wave-front multiplexer 213 can be, but not limited to, hardware, such as a device of four-by-four Butler matrix or a device performing any transformation of a four-by-four orthogonal matrix.

Referring to FIG. 5A, each of the optical transmit devices or transmitters 520 _(a), 520 _(b), 520 _(c) and 520 _(d) can be a laser generator, wherein the laser generator can emit a distributed feedback laser (DFB laser), a Fabry-perot laser (F-P laser) or a vertical cavity surface emitting laser (VCSEL) to the mode-group diversity multiplexing (MGDM) device 516. Upon receiving the digital signals Y₁, Y₂, Y₃ and Y₄ input in parallel from multiple parallel output ports 3 _(a)-3 _(d) of the wave-front multiplexer 513 respectively, the optical transmit devices 520 _(a), 520 _(b), 520 _(c) and 520 _(d) emit four individual optical signals T₁-T₄ based on the digital signals Y₁, Y₂, Y₃ and Y₄ to the MGDM device 516, wherein the optical signal T₁ carries information associated with the digital signal Y₁, the optical signal T₂ carries information associated with the digital signal Y₂, the optical signal T₃ carries information associated with the digital signal Y₃, and the optical signal T₄ carries information associated with the digital signal Y₄. The MGDM device 516 has been proposed as a way of creating parallel communication channels over the multimode fiber (MMF) 524. The MGDM 516 has been proved as an efficient scheme to overcome the limited bandwidth of the multimode fiber (MMF) 524. MGDM device 516 can multiplex the optical signals T₁-T₄ into different mode groups of light, propagating with different angles in the MMF 524, wherein each mode groups of the light are used to carry different information so that the data throughput is increased without having additional bandwidth.

Referring to FIG. 5A, upon receiving the different mode groups of the light output from the MGDM device 516 and propagating over the MMF 524, the mode-group diversity demultiplexing (MGDDM) device 518 demultiplexes the different mode groups of the light based on the time when the different mode groups of the light approach the MGDDM device 518 and on the angles of the different mode groups of the light into multiple optical signals V₁-V₄ received by the optical detectors 522 a, 522 b, 522 c and 522 d. Upon respectively receiving the four optical signals V₁-V₄ output in parallel from the MGDDM device 518 respectively, the four optical detectors 522 a, 522 b, 522 c and 522 d can send four digital signals W₁, W₂, W₃ and W₄ to the equalizer 231, respectively. The digital signal W₁ carries information associated with the optical signal V₁, the digital signal W₂ carries information associated with the optical signal V₂, the digital signal W₃ carries information associated with the optical signal V₃, and the digital signal W₄ carries information associated with the optical signal V₄.

Next, referring to FIG. 5A, the digital signals W₁, W₂, W₃ and W₄ are transmitted in parallel into four input ports 10 a, 10 b, 10 c and 10 d of the equalizer 231 through, e.g., four parallel channels, such as wireless channels or physical channels. The input ports 10 a, 10 b, 10 c and 10 d are arranged in parallel for receiving the digital signals W₁, W₂, W₃ and W₄, respectively. After the digital signals W₁, W₂, W₃ and W₄ are transmitted in parallel into the equalizer 231, the above optimizing and equalizing process, as illustrated in FIGS. 1B and 1C, is performed such that the digital signals W₁, W₂, W₃ and W₄ can be compensated to be multiplied by four respective weightings by the equalizer 231, wherein the four respective weightings of the equalizer 231 can be adjusted based on a control signal CS, output from the optimizer 235 and input into the equalizer 231. The optimizing and equalizing process can be referred to as the optimizing and equalizing process as illustrated in FIGS. 1B and 1C. After the optimizing and equalizing process, the equalizer 231 outputs four equalized digital signals S₁, S₂, S₃ and S₄, respectively, from its output ports 11 a, 11 b, 11 c and 11 d. The equalized digital signal S₁ is created by the equalizer 231 multiplying the digital signal W₁ by a weighting of the equalizer 231, the equalized digital signal S₂ is created by the equalizer 231 multiplying the digital signal W₂ by another weighting of the equalizer 231, the equalized digital signal S₃ is created by the equalizer 231 multiplying the digital signal W₃ by another weighting of the equalizer 231, and the equalized digital signal S₄ is created by the equalizer 231 multiplying the digital signal W₄ by the other weighting of the equalizer 231. Next, the equalized digital signals S₁, S₂, S₃ and S₄ are transmitted in parallel into input ports 6 a, 6 b, 6 c and 6 d of the wave-front demultiplexer 232 through four parallel signal paths between the output ports 11 a, 11 b, 11 c and 11 d of the equalizer 231 and the input ports 6 a, 6 b, 6 c and 6 d of the wave-front demultiplexer 232. Each of the four respective weightings of the equalizer 231 can be, but not limited to, a complex value such that the equalized signals S₁, S₂, S₃ and S₄ can be rotated precisely to become in phase. In this case, the equalizer 231 can be performed by the narrow band equalizer, as illustrated in FIG. 1C. The narrow band equalizer 231 can provide phase and amplitude modifications to each of the signals W₁, W₂, W₃ and W₄ featuring a constant phase shift and a constant amplitude attenuation across a narrow frequency band. Alternatively, the equalizer 231 can be performed by the broadband equalizer, as illustrated in FIG. 1C. The broadband equalizer 231 can provide phase and amplitude modifications to each of the signals W₁, W₂, W₃ and W₄ featuring a constant phase shift and a constant amplitude attenuation in each sub-band across a broad frequency band, but the phase shift and amplitude attenuation in one sub-band across the broad frequency band is different from those in the other sub-bands across the broad frequency band.

Referring to FIG. 5A, upon receiving, in parallel, the equalized digital signals S₁, S₂, S₃ and S₄ output in parallel from the equalizer 531, the wave-front demultiplexer 232 extracts multiple coherently combined digital signals Z₁, Z₂, Z₃ and Z₄, which are substantially equal to the digital signals X₁, X₂, X₃ and X₄, respectively, or to the digital signals X₁, X₂, X₃ and X₄ multiplied by the same scalar, respectively, from the digital signals S₁, S₂, S₃ and S₄ by the above-mentioned wave-front demultiplexing transform, and outputs the digital signals Z₁, Z₂, Z₃ and Z₄ in parallel, which can be referred to as the description illustrated in FIGS. 1A and 1E. In this case, as illustrated in FIG. 1E, the number of I is equal to 4. The wave-front demultiplexer 232 has 4*4 computing units and four summing processors. The computing units form a processor array with four rows and four columns. The input signals S₁-S₄ can be received by the computing units in the respective four columns in the processor array. Upon receiving the input signals S₁-S₄, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The four summing processors can output the four signals Z₁-Z₄ each combined with the weighted signals output from the computing units in a corresponding one of the four rows in the processor array. The digital signals Z₁, Z₂, Z₃ and Z₄ can be, but not limited to, four IF digital signals or four RF digital signals. Each of the digital signals Z₁, Z₂, Z₃ and Z₄ is a linear combination, i.e. weighted sum, each combined with the digital signals S₁, S₂, S₃ and S₄ multiplied by respective weightings, and distributions of the weightings of any two input components in all digital signals Z₁, Z₂, Z₃ and Z₄ are orthogonal, which can be referred to as the description illustrated in FIG. 1A.

The wave-front demultiplexer 232 can be, but not limited to, embedded in a processor. The wave-front demultiplexer 232 can be hardware achieving the wave-front demultiplexing transform, such as IFFT chip, a component for four-by-four inverse Butler matrix, or a device performing inverse Fourier transformation, inverse discrete Fourier transformation, inverse Hartley transformation, Hadamard transformation, any other inverse Fourier-related transformation, or any transformation of a four-by-four orthogonal matrix. Alternatively, the function of the wave-front demultiplexer 232 can be realized by software installed in and performed by the processor, wherein the software can perform the above wave-front demultiplexing transform.

The optimizer 235 can be in a signal path between the output ports 7 a, 7 b, 7 c and 7 d and the equalizer 231 (only one signal path between the output port 7 d and the equalizer 231 is shown in FIG. 5A). The flow chart of the optimizing and equalizing process shown in FIG. 1C can be applied to the embodiment illustrated in FIG. 5A.

The equalizer 231, the wave-front demultiplexer 232 and the optimizer 235 can be, but not limited to, embedded in a processor 230, such as single integrated circuit chip or single chip package. The equalizer 231 can be hardware or can be realized by software installed in and performed by the processor 230. The optimizer 235 can be hardware or can be realized by software installed in and performed by the processor 230.

Referring to FIG. 5C, the system 500 features point-to-point communications. The system 500 shown in FIG. 5C is similar to the system 500 illustrated in FIG. 5A except that the system 500 illustrated in FIG. 5C further includes a 1-to-3 time-domain demultiplexer (TDDM) 538 and the 3-to-1 time-domain multiplexer (TDM) 540. The 1-to-3 TDDM 538 includes an input port receiving a digital signal A₀ and three output ports outputting the three digital signals X₁, X₂ and X₃. The TDDM is defined herein to divide an input signal having a high bandwidth sampled at a high sampling rate into multiple output signals each having a low bandwidth sampled at a low sampling rate. For example, in this embodiment, the 1-to-3 TDDM 538 can divide an input digital signal A₀ having a bandwidth of J sampled at a sampling rate of K into three output digital signals X₁, X₂ and X₃, each having a frequency bandwidth of J/3 sampled at a sampling rate of K/3, passing through three parallel signal paths, such as physical or wireless channels, coupled to the wave-front multiplexer 213.

The 3-to-1 TDM 540 includes three input ports receiving the digital signals Z₁, Z₂ and Z₃ and an output port outputting a digital signal B₀. The 3-to-1 TDM 540 can combine or integrate the input signals Z₁, Z₂ and Z₃, each having a frequency bandwidth of J/3 sampled at a sampling rate of K/3, passing through three parallel signal paths, such as physical or wireless channels, coupled to the wave-front demultiplexer 532 into an output signal B₀ having a frequency bandwidth of J sampled at a sampling rate of K.

The output signal B₀ is reconstituted by combining or integrating the three recovered signals Z₁, Z₂ and Z₃ into one with high data flow rate through the TDM 540. The output signal B₀ is substantially equal to the input signal A₁. As a result, the input signal A₀ will be fully recovered.

For more elaboration, a 1-to-M TDDM (TDDM) denotes that it can divide an input signal, having a frequency bandwidth of J sampled at a sampling rate of K, into the number M of output signals, each having a frequency bandwidth of J/M sampled at a sampling rate of K/M. For example, the 1-to-M TDDM can be, but not limited to, a 1-to-3 TDDM 538 shown in FIG. 5C, and the 1-to-3 time-domain demultiplexer (TDDM) 538 denotes that it can divide an input signal, having a frequency bandwidth of J sampled at a sampling rate of K, into three output signals, each having a frequency bandwidth of J/3 sampled at a sampling rate of K/3. An M-to-1 TDM denotes that it can combine or integrate the number M of input signals, each having a frequency bandwidth of J/M sampled at a sampling rate of K/M, into an output signal having a frequency bandwidth of J sampled at a sampling rate of K. For example, the M-to-1 TDM can be, but not limited to, a 3-to-1 time-domain multiplexer 540 shown in FIG. 5C, and the 3-to-1 time-domain multiplexer 540 denotes that it can combine or integrate three input signals, each having a frequency bandwidth of J/3 sampled at a sampling rate of K/3, into an output signal having a frequency bandwidth of J sampled at a sampling rate of K.

Next, referring to FIG. 5C, the digital signals X₁, X₂ and X₃ output from the 1-to-3 TDDM 538 and the pilot or diagnostic signal X₄ can be transmitted to the wave-front multiplexer 213 and then can be processed as illustrated in FIG. 5A until the digital signals Z₁-Z₄ are output from the wave-front demultiplexer 232. Upon the wave-front demultiplexer 232 outputting the digital signals Z₁-Z₄, the 3-to-1 time-domain multiplexer 540 can combine or integrate the digital signals Z₁-Z₃, each having a frequency bandwidth of J/3 sampled at a sampling rate of K/3, into an output signal B₀ having a frequency bandwidth of J sampled at a sampling rate of K.

Referring to FIG. 5D, the system 500 is for a multipoint-to-point design, but the system 500 shown in FIG. 5D is still similar to the system 500 illustrated in FIG. 5B except that the system 500 illustrated in FIG. 5D uses the number Nt of signal transmitting sources, such as including a first transmitting source L₁ processing one, i.e. X₁, of the digital signals X₁, X₂ and X₃, and a second transmitting source L₂ processing two, i.e. X₂ and X₃, of the digital signals X₁, X₂ and X₃, and the number Nr of signal receiving sources, such as such as including only one receiving source outputting the three digital signals Z₁, Z₂ and Z₃ substantially equal to the digital signals X₁, X₂ and X₃ respectively or to the digital signals X₁, X₂ and X₃ multiplied by the same scalar, respectively, wherein the number of Nt could be any number equal to or greater than 2, 3, 4, 5, 6, 7, 8, 9 or 10, and could be greater than the number of Nr that could be one in this embodiment. The number Nt of the transmitting sources have the same wave-front multiplexer as one another or each other and use different input ports in sequence for receiving different extraneous signals. For example, referring to FIG. 5D, the two transmitting sources L₁ and L₂ contains two wave-front multiplexers 213 a and 213 b each having the same architecture as each other, and the wave-front multiplexers 213 a and 213 b use different input ports in sequence for receiving the different extraneous signals X₁, X₂ and X₃, wherein the wave-front multiplexer 213 a uses the topmost port for receiving the extraneous signals X₁, but the wave-front multiplexer 213 b uses the middle two ports, for receiving the extraneous signals X₂ and X₃ output from a 1-2 time domain demultiplexer (TDDM), different in sequence from the port of the wave-front multiplexer 213 a for receiving the extraneous signals X₁. In this case, referring to FIG. 5C, the same pilot or diagnostic signals X₄ carrying the same information can be input to the bottommost ports of the wave-front multiplexers 213 a and 213 b. The other ports of the wave-front multiplexers 213 a and 213 b can be connected to a ground reference for receiving ground signals. The number Nt of the signal transmitting sources contains the number Nt of mode-group diversity multiplexing (MGDM) device, wherein the mode groups of the lights output from output ports of the MGDM devices in the same mode can be combined together. For example, the mode group of the light carrying information associated with the signal X₁ input to the topmost one of the input ports of the MGDM device 516 a can be combined with the mode group of the light carrying information associated with the ground signal input to the topmost one of the input ports of the MGDM device 516 b. The mode group of the light carrying information associated with the ground signal input to the second topmost one of the input ports of the MGDM device 516 a can be combined with the mode group of the light carrying information associated with the signal X₂ input to the second topmost one of the input ports of the MGDM device 516 b. The mode group of the light carrying information associated with the ground signal input to the third topmost one of the input ports of the MGDM device 516 a can be combined with the mode group of the light carrying information associated with the signal X₃ input to the third topmost one of the input ports of the MGDM device 516 b. The mode group of the light carrying information associated with the signal X₄ input to the bottommost one of the input ports of the MGDM device 516 a can be combined with the mode group of the light carrying information associated with the signal X₄ input to the bottommost one of the input ports of the MGDM device 516 b.

The number Nr of the receiving sources use different output ports in sequence for outputting different signals. For example, referring to FIG. 5D, the wave-front demultiplexer 232 uses a topmost output port for outputting the digital signal Z₁, substantially equal to the digital signal X₁ or to the digital signal X₁ multiplied by the same scalar, in the same sequence as the input port of the wave-front multiplexer 213 a for receiving the digital signal X₁. The wave-front demultiplexer 232 uses a second topmost output port for outputting the digital signal Z₂, substantially equal to the digital signal X₂ or to the digital signal X₂ multiplied by the same scalar, in the same sequence as the input port of the wave-front multiplexer 213 b for receiving the digital signal X₂. The wave-front demultiplexer 232 uses a third topmost output port for outputting the digital signal Z₃, substantially equal to the digital signal X₃ or to the digital signal X₃ multiplied by the same scalar, in the same sequence as the input port of the wave-front multiplexer 213 b for receiving the digital signal X₃. The wave-front demultiplexer 232 uses a bottommost output port for outputting the digital pilot or diagnostic signal Z₄, substantially equal to the digital signal X₄ or to the digital signal X₄ multiplied by the same scalar, in the same sequence as the input port of the wave-front multiplexer 213 a for receiving the digital signal X₄ and as the input port of the wave-front multiplexer 213 b for receiving the digital signal X₄. A method for processing signals or data streams by using the system 500 shown in FIG. 5D is described below. In sources L₁, there are an extraneous digital signal X₁, the digital pilot or diagnostic signal X₄ and two ground signals input in parallel to input ports of the wave-front multiplexer 213 a through, e.g., four parallel channels, such as wireless channels or physical channels, wherein the middle two of the input ports of the wave-front multiplexer 213 a are connected to a ground reference for receiving the two ground signals. The digital pilot or diagnostic signal X₄ may have a single frequency and fixed amplitude. Alternatively, the digital pilot or diagnostic signal X₄ could change based on time or could be any signal known by the system 500. The extraneous digital signal X₁ is unknown by the system 500 and input into the system 500 from an extraneous system. The two ground signals represent no extraneous signals input to the input ports of the wave-front multiplexer 213 a.

Next, the wave-front multiplexer 213 a performs the above wave-front multiplexing transform to process the digital signals X₁ and X₄ and the two ground signals into multiple linear combinations, each combined with the digital signals X₁ and X₄ and the two ground signals multiplied by respective weightings, represented by four digital signals Y_(1a), Y_(2a), Y_(3a) and Y_(4a), which can referred to as FIGS. 1A and 1D. In this case, as illustrated in FIG. 1D, the number of H is equal to 4. The wave-front multiplexer 213 a has 4*4 computing units and four summing processors. The computing units form a processor array with four rows and four columns. The digital signals X₁ and X₄ and the two ground signals can be received by the computing units in the respective four columns in the processor array. Upon receiving the input signals X₁ and X₄ and the two ground signals, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The four summing processors can output the four signals Y_(1a), Y_(2a), Y_(3a) and Y_(4a) each combined with the weighted signals output from the computing units in a corresponding one of the four rows in the processor array. The digital signals X₁ and X₄ can be, but not limited to, four IF digital signals or four RF digital signals.

Next, the digital signals Y_(1a), Y_(2a), Y_(3a) and Y_(4a) output from the wave-front multiplexer 213 a are respectively transmitted into four input ports of the optical transmit device 520 a ₁, 520 b ₁, 520 c ₁ and 520 d ₁ through, e.g., four parallel channels, such as wireless channels or physical channels. Next, upon receiving the digital signals Y_(1a), Y_(2a), Y_(3a) and Y_(4a) output in parallel from four parallel output ports of the wave-front multiplexer 213 a, the optical transmit device 520 a ₁, 520 b ₁, 520 c ₁ and 520 d ₁ emit four individual optical signals T_(1a)-T_(4a) based on the digital signals Y_(1a)-Y_(4a) to a MGDM device 516 a that can be referred as the MGDM device 516 as illustrated in FIG. 5A, wherein the optical signal T_(1a) carries information associated with the digital signal Y_(1a), the optical signal T_(2a) carries information associated with the digital signal Y_(2a), the optical signal T_(1a) carries information associated with the digital signal Y_(3a), and the optical signal T_(4a) carries information associated with the digital signal Y_(4a). Upon receiving the optical signals T_(1a)-T_(4a), the MGDM device 516 a can multiplex the optical signals T_(1a)-T_(4a) into different mode groups of light, propagating with different angles in the MMF 524.

The sources L₂ includes a 1-to-2 time-domain demultiplexer (TDDM) 538 having an input port receiving a digital signal A₀ and two output ports outputting two digital signals X₂ and X₃. The 1-to-2 TDDM 538 can divide an extraneous digital signal A₀ having a frequency bandwidth of J sampled at a sampling rate of K into two output digital signals X₂ and X₃, each having a bandwidth of J/2 sampled at a sampling rate of K/2, passing through two parallel signal paths, such as physical or wireless channels, coupled to the wave-front multiplexer 213 b.

The digital signals X₂ and X₃, the pilot or diagnostic signal X₄ and a ground signal can be input in parallel to input ports of the wave-front multiplexer 513 b through, e.g., four parallel channels, such as wireless channels or physical channels, wherein the topmost one of the input ports of the wave-front multiplexer 213 b is connected to a ground reference for receiving the ground signal. The signals X₂ and X₃ could be independent from each other. The pilot or diagnostic signal X₄ input to the wave-front multiplexer 513 b can be the same as the pilot or diagnostic signal X₄ input to the wave-front multiplexer 513 a. The pilot or diagnostic signals may have a single frequency and fixed amplitude. Alternatively, the pilot or diagnostic signals X₄ could change based on time or could be any signal known by the system 500. Instead, the extraneous digital signals X₂ and X₃ input to the wave-front multiplexer 513 b and the extraneous digital signal X₁ input to the wave-front multiplexer 513 a are unknown by the system 500 and input into the system 500 from an extraneous system. The ground signal represents no extraneous signal input to the input port of the wave-front multiplexer 213 b.

Next, the wave-front multiplexer 213 b performs the above wave-front multiplexing transform to process the digital signals X₂, X₃ and X₄ and the ground signal into multiple linear combinations, each summed with the digital signals X₂, X₃ and X₄ and the ground signal multiplied by respective weightings, represented by four digital signals Y_(1b), Y_(2b), Y_(3b) and Y_(4b), which can referred to as FIGS. 1A and 1D. In this case, as illustrated in FIG. 1D, the number of H is equal to 4. The wave-front multiplexer 213 b has 4*4 computing units and four summing processors. The computing units form a processor array with four rows and four columns. The digital signals X₂, X₃ and X₄ and the ground signal can be received by the computing units in the respective four columns in the processor array. Upon receiving the input signals X₂, X₃ and X₄ and the ground signal, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The four summing processors can output the four signals Y_(1b), Y_(2b), Y_(3b) and Y_(4b) each summed with the weighted signals output from the computing units in a corresponding one of the four rows in the processor array. The digital signals X₂, X₃ and X₄ can be, but not limited to, four IF digital signals or four RF digital signals.

Next, the digital signals Y_(1b), Y_(2b), Y_(3b) and Y_(4b) output from the wave-front multiplexer 213 b are respectively transmitted into four input ports of the optical transmit device 520 a ₂, 520 b ₂, 520 c ₂ and 520 d ₂ through, e.g., four parallel channels, such as wireless channels or physical channels. Next, upon receiving the digital output signals Y_(1b), Y_(2b), Y_(3b) and Y_(4b) output in parallel from four parallel output ports of the wave-front multiplexer 513 b, the optical transmit device 520 a ₂, 520 b ₂, 520 c ₂ and 520 d ₂ emit four individual optical signals T_(1b)-T_(4b) based on the digital signals Y_(1b)-Y_(4b) to a MGDM device 516 b that can be referred as the MGDM device 516 as illustrated in FIG. 5A, wherein the optical signal T_(1b) carries information associated with the digital signal Y_(1b), the optical signal T_(2b) carries information associated with the digital signal Y_(2b), the optical signal T_(3b) carries information associated with the digital signal Y_(3b), and the optical signal T_(4b) carries information associated with the digital signal Y_(4b). Upon receiving the optical signals T_(1b)-T_(4b), the MGDM device 516 b can multiplex the optical signals T_(1b)-T_(4b) into different mode groups of light, propagating with different angles in the MMF 524.

Referring to FIG. 5D, upon receiving the different mode groups of the light output from the MGDM devices 516 a and 516 b and propagating over the MMF 524, the mode-group diversity demultiplexing (MGDDM) device 518 demultiplexes the different mode groups of the light based on the time when the different mode groups of the light approach the MGDDM device 518 and on the angles of the different mode groups of the light into multiple optical signals V₁-V₄ received by the optical detectors 522 a, 522 b, 522 c and 522 d. Upon respectively receiving the four optical signals V₁-V₄ output in parallel from the MGDDM device 518, the four optical detectors 522 a, 522 b, 522 c and 522 d can send four digital signals W₁, W₂, W₃ and W₄, to the equalizer 231, respectively. The digital signal W₁ carries information associated with the optical signal V₁, the digital signal W₂ carries information associated with the optical signal V₂, the digital signal W₃ carries information associated with the optical signal V₃, and the digital signal W₄ carries information associated with the optical signal V₄.

Next, referring to FIG. 5D, the digital signals W₁, W₂, W₃ and W₄ are transmitted in parallel into four input ports 10 a, 10 b, 10 c and 10 d of the equalizer 231 through, e.g., four parallel channels, such as wireless channels or physical channels. The input ports 10 a, 10 b, 10 c and 10 d are arranged in parallel for receiving the digital signals W₁, W₂, W₃ and W₄, respectively. After the digital signals W₁, W₂, W₃ and W₄ are transmitted in parallel into the equalizer 231, the above optimizing and equalizing process, as illustrated in FIGS. 1B and 1C, is performed such that the digital signals W₁, W₂, W₃ and W₄ can be compensated to be multiplied by four respective weightings by the equalizer 231, wherein the four respective weightings of the equalizer 231 can be adjusted based on a control signal CS, output from the optimizer 235 and input into the equalizer 231. The optimizing and equalizing process can be referred to as the optimizing and equalizing process as illustrated in FIGS. 1B and 1C. After the optimizing and equalizing process, the equalizer 231 outputs four equalized digital signals S₁, S₂, S₃ and S₄, respectively, from its output ports 11 a, 11 b, 11 c and 11 d. The equalized digital signal S₁ is created by the equalizer 231 multiplying the digital signal W₁ by a weighting of the equalizer 231, the equalized digital signal S₂ is created by the equalizer 231 multiplying the digital signal W₂ by another weighting of the equalizer 231, the equalized digital signal S₃ is created by the equalizer 231 multiplying the digital signal W₃ by another weighting of the equalizer 231, and the equalized digital signal S₄ is created by the equalizer 231 multiplying the digital signal W₄ by the other weighting of the equalizer 231. Next, the equalized digital signals S₁, S₂, S₃ and S₄ are transmitted in parallel into input ports 6 a, 6 b, 6 c and 6 d of the wave-front demultiplexer 232 through four parallel signal paths between the output ports 11 a, 11 b, 11 c and 11 d of the equalizer 231 and the input ports 6 a, 6 b, 6 c and 6 d of the wave-front demultiplexer 232. Each of the four respective weightings of the equalizer 231 can be, but not limited to, a complex value such that the equalized signals S₁, S₂, S₃ and S₄ can be rotated precisely to become in phase. In this case, the equalizer 231 can be performed by the narrow band equalizer, as illustrated in FIG. 1C. The narrow band equalizer 231 can provide phase and amplitude modifications to each of the signals W₁, W₂, W₃ and W₄ featuring a constant phase shift and a constant amplitude attenuation across a narrow frequency band. Alternatively, the equalizer 231 can be performed by the broadband equalizer, as illustrated in FIG. 1C. The broadband equalizer 231 can provide phase and amplitude modifications to each of the signals W₁, W₂, W₃ and W₄ featuring a constant phase shift and a constant amplitude attenuation in each sub-band across a broad frequency band, but the phase shift and amplitude attenuation in one sub-band across the broad frequency band is different from those in the other sub-bands across the broad frequency band.

Next, referring to FIG. 5D, upon receiving, in parallel, the equalized digital signals S₁, S₂, S₃ and S₄ output in parallel from the equalizer 531, the wave-front demultiplexer 232 extracts multiple coherently combined digital signals Z₁, Z₂, Z₃ and Z₄, which are substantially equal to the digital signals X₁, X₂, X₃ and X₄ respectively or to the digital signals X₁, X₂, X₃ and X₄ multiplied by the same scalar, respectively, from the digital signals S₁, S₂, S₃ and S₄ by the above-mentioned wave-front demultiplexing transform, and outputs the digital signals Z₁, Z₂, Z₃ and Z₄ in parallel, which can be referred to as the description illustrated in FIGS. 1A and 1E. In this case, as illustrated in FIG. 1E, the number of I is equal to 4. The wave-front demultiplexer 232 has 4*4 computing units and four summing processors. The computing units form a processor array with four rows and four columns. The input signals S₁-S₄ can be received by the computing units in the respective four columns in the processor array. Upon receiving the input signals S₁-S₄, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The four summing processors can output the four signals Z₁-Z₄ each combined with the weighted signals output from the computing units in a corresponding one of the four rows in the processor array. The digital signals Z₁, Z₂, Z₃ and Z₄ can be, but not limited to, four IF digital signals or four RF digital signals. Each of the digital signals Z₁, Z₂, Z₃ and Z₄ is a linear combination, i.e. weighted sum, each summed with the digital signals S₁, S₂, S₃ and S₄ multiplied by respective weightings, and distributions of the weightings of any two input components in all digital signals Z₁, Z₂, Z₃ and Z₄ are orthogonal, which can be referred to as the description illustrated in FIG. 1A.

Next, the 2-to-1 TDM 540 can combine or integrate the two input signals Z₂ and Z₃, each having a bandwidth of J/2 sampled at a sampling rate of K/2, passing through two parallel signal paths, such as physical or wireless channels, coupled to the wave-front demultiplexer 532 into an output signal B₀ having a bandwidth of J sampled at a sampling rate of K.

The output signal B₀ is reconstituted by combining the two recovered signals Z₂ and Z₃ into one with high data flow rate through a time-domain demultiplexer 540. The output signal B₀ is substantially equal to the input signal A₀ or to the input signal A₀ multiplied by the same scalar as the input signal X₁ multiplied by. As a result, the input signal A₀ will be fully recovered due to the above optimizing and equalizing process.

Referring to FIG. 5E, a system 500 shown in FIG. 5E is similar to the system 500 illustrated in FIG. 5C except that the system 500 illustrated in FIG. 5E further includes a 1-to-250 time-domain demultiplexer 538, eight 32-to-1 time-domain multiplexers 542 a-542 h, eight 1-to-32 time-domain demultiplexers 544 a-544 h, and a 250-to-1 time-domain multiplexer 540. The 1-to-250 time-domain demultiplexer 538 divides an input signal A₁, having a frequency bandwidth of J sampled at a sampling rate of K, into two-hundred-and-fifty output signals X₁-X₂₅₀, each having a frequency bandwidth of J/250 sampled at a sampling rate of K/250 and outputs the signals X₁-X₂₅₀ from its two-hundred-and-fifty output ports. The description of the above-mentioned M-to-1 time-domain multiplexer can be applied to the 250-to-1 time-domain multiplexer 540.

Next, the signals X₁-X₂₅₀ and six signals X₂₅₁-X₂₅₆ are transmitted in parallel to the wave-front multiplexer 213. Each of the signals X₂₅₁-X₂₅₆ is a stream of pilot codes. Each of the signals X₂₅₁-X₂₅₆, for example, may have a single frequency and fixed amplitude. Alternatively, the six signal X₂₅₁-X₂₅₆ could change based on time or could be any signal known by the system 500. The signals X₁-X₂₅₀ are unknown by the system 500. The extraneous signal A₁ is unknown by the system 500 and input into the system 500 from an extraneous system.

Next, the wave-front multiplexer 213 performs the above-mentioned wave-front multiplexing transformation to process the two-hundred-and-fifty-six signals X₁-X₂₅₆ into two-hundred-and-fifty-six linear combinations, each combined with the signals X₁-X₂₅₆ multiplied by respective weightings, represented by two-hundred-and-fifty-six signals Y₁-Y₂₅₆, which can be referred to as the description illustrated in FIG. 1D. In this case, the number of H is equal to 256. The wave-front multiplexer 213 may include 256*256 computing units and 256 summing processors. The computing units form a processor array with 256 rows and 256 columns. The input signals X₁-X₂₅₆ can be received by the computing units in the respective 256 columns in the processor array. Upon receiving the input signals X₁-X₂₅₆, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The 256 summing processors can output the 256 signals Y₁-Y₂₅₆ each combined with the weighted signals output from the computing units in a corresponding one of the 256 rows in the processor array. The signals X₁-X₂₅₆ can be, but not limited to, 256 IF digital signals or 256 RF digital signals.

The wave-front multiplexer 213 can be, but not limited to, embedded or integrated in a module or processor. The wave-front multiplexer 213 can be, but not limited to, implemented by hardware which performing the above wave-front multiplexing transformation, such as FFT chip, 256×256 Butler matrix, or a device performing a transformation of a 256-by-256 orthogonal matrix.

Next, eight sets of thirty-two ones of the two-hundred-and-fifty-six signals Y₁-Y₂₅₆ are respectively transmitted in parallel to the eight 32-to-1 time-domain multiplexers 542 a-542 h through, e.g., multiple parallel signal paths, multiple parallel physical channels or multiple parallel wireless channels. The six 32-to-1 time-domain multiplexers 542 b-542 g are not shown in FIG. 5E. Next, each of the eight 32-to-1 time-domain multiplexers 542 a-542 h combines or integrates a corresponding set of the received thirty-two ones of the two-hundred-and-fifty-six signals Y₁-Y₂₅₆ into a corresponding one of eight output signals G₁-G₈ and outputs the corresponding one of the eight output signals G₁-G₈ to a corresponding one of the eight optical transmit devices or transmitters 520 a-520 h. The description of the above-mentioned U-to-1 time-domain multiplexer can be applied to each of the 32-to-1 time-domain multiplexers 542 a-542 h. For example, the 32-to-1 time-domain multiplexer 542 a combines or integrates the received thirty-two signals Y₁-Y₃₂ into the output signal G₁ and outputs the output signal G₁ to the optical transmit device 520 a. The description of the above-mentioned U-to-1 time-domain multiplexer can be applied to each of the 32-to-1 time-domain multiplexers 542 a-542 h. The 32-to-1 time-domain multiplexer 542 h combines or integrates the received thirty-two signals Y₂₂₅-Y₂₅₆ into the output signal G₈ and outputs the output signal G₈ to the optical transmit device 520 h. The description of the above-mentioned U-to-1 time-domain multiplexer can be applied to each of the 32-to-1 time-domain multiplexers 542 a-542 h.

After the eight output signals G₁-G₈ are respectively input in parallel to the eight optical transmit devices 520 a-520 h, the eight optical transmit devices 520 a-520 h emit eight individual optical signals T₁-T₈ based on the signals G₁-G₈ to the MGDM device 516, respectively. The optical signal T₁ carries information associated with the digital signal G₁. The optical signal T₂ carries information associated with the digital signal G₂. The optical signal T₃ carries information associated with the digital signal G₃. The optical signal T₄ carries information associated with the digital signal G₄. The optical signal T₅ carries information associated with the digital signal G₅. The optical signal T₆ carries information associated with the digital signal G₆. The optical signal T₇ carries information associated with the digital signal G₇. The optical signal T₈ carries information associated with the digital signal G₈. Each of the optical transmit devices 520 a-520 h can be, but not limited to, a laser generator and emits a distributed feedback laser (DFB laser), a Fabry-perot laser (F-P laser) or a vertical cavity surface emitting laser (VCSEL) featuring the optical signals T1-T8 to the MGDM device 516.

The MGDM device 516 has been proposed as a way of creating parallel, independent communication channels over the multimode fiber 524. The MGDM 516 has been proved as an efficient scheme to overcome the limited bandwidth of the multimode fiber 524. The MGDM device 516 can multiplex the optical signals T₁-T₈ into different mode groups of light, propagating with different angles in the MMF 524, wherein each mode groups of the light are used to carry different information so that the data throughput is increased without having additional bandwidth. The signals G₂-G₇ are not shown in FIG. 5E.

Referring to FIG. 5E, upon receiving the different mode groups of the light output from the MGDM device 516 and propagating over the MMF 524, the mode-group diversity demultiplexing (MGDDM) device 518 demultiplexers the different mode groups of the light based on the time when the different mode groups of the light approach the MGDDM device 518 and on the angles of the different mode groups of the light into multiple optical signals V₁-V₈ received by the eight optical detectors 522 a-522 h. Upon respectively receiving the eight optical signals V₁-V₈ output in parallel from the MGDDM device 518, the eight optical detectors 522 a-522 h send eight digital signals H₁-H₈ to the eight 1-to-32 time-domain demultiplexers 544 a-544 h, respectively. The digital signal H₁ carries information associated with the optical signal V₁. The digital signal H₂ carries information associated with the optical signal V₂. The digital signal H₃ carries information associated with the optical signal V₃. The digital signal H₄ carries information associated with the optical signal V₄. The digital signal H₅ carries information associated with the optical signal V₅. The digital signal H₆ carries information associated with the optical signal V₆. The digital signal H₇ carries information associated with the optical signal V₇. The digital signal H₈ carries information associated with the optical signal V₈. The six 1-to-32 time-domain demultiplexers 544 b-544 g and the six signals H₂-H₇ are not shown in FIG. 5E.

Next, the 1-to-32 TDDM 544 a divides the input digital signal H₁ into thirty-two output digital signals W₁-W₃₂ passing through thirty-two parallel signal paths or channels coupled to the Equalizer 231. The 1-to-32 TDDM 544 b divides the input digital signal H₂ into thirty-two output digital signals W₃₃-W₆₄ passing through thirty-two parallel signal paths or channels coupled to the Equalizer 231. The 1-to-32 TDDM 544 c divides the input digital signal H₃ into thirty-two output digital signals W₆₅-W₉₆ passing through thirty-two parallel signal paths or channels coupled to the Equalizer 231. The 1-to-32 TDDM 544 d divides the input digital signal H₄ into thirty-two output digital signals W₉₇-W₁₂₈ passing through thirty-two parallel signal paths or channels coupled to the Equalizer 231. The 1-to-32 TDDM 544 e divides the input digital signal H₅ into thirty-two output digital signals W₁₂₉-W₁₆₀ passing through thirty-two parallel signal paths or channels coupled to the Equalizer 231. The 1-to-32 TDDM 544 f divides the input digital signal H₆ into thirty-two output digital signals W₁₆₁-W₁₉₂ passing through thirty-two parallel signal paths or channels coupled to the Equalizer 231. The 1-to-32 TDDM 544 g divides the input digital signal H₇ into thirty-two output digital signals W₁₉₃-W₂₂₄ passing through thirty-two parallel signal paths or channels coupled to the Equalizer 231. The 1-to-32 TDDM 544 h divides the input digital signal H₈ into thirty-two output digital signals W₂₂₅-W₂₅₆ passing through thirty-two parallel signal paths or channels coupled to the Equalizer 231.

Next, referring to FIG. 5E, the two-hundred-and-fifty-six digital signals W₁-W₂₅₆ are transmitted in parallel into the equalizer 231 through, e.g., two-hundred-and-fifty-six parallel signal paths, wireless channels or physical channels. After the digital signals W₁-W₂₅₆ are transmitted in parallel into the equalizer 231, an optimizing and equalizing process is performed such that the digital signals W₁-W₂₅₆ can be compensated to be multiplied by two-hundred-and-fifty-six respective weightings by the equalizer 231, wherein the respective weightings of the equalizer 231 can be adjusted based on a control signal CS output from the optimizer 235 and input into the equalizer 231. The optimizing and equalizing process can be referred to as the optimizing and equalizing process as illustrated in FIG. 1C. After the optimizing and equalizing process, the equalizer 231 outputs two-hundred-and-fifty-six equalized digital signals S₁-S₂₅₆ from its output ports, respectively. Each of the equalized digital signals S₁-S₂₅₆ is created by the equalizer 231 multiplying the corresponding one of the digital signals W₁-W₂₅₆ by a weighting of the equalizer 231. For example, the equalized digital signal S₁ is created by the equalizer 231 multiplying the digital signal W₁ by a weighting of the equalizer 231, and the equalized digital signal S₈ is created by the equalizer 231 multiplying the digital signal W₈ by another weighting of the equalizer 231. Each of the 256 respective weightings of the equalizer 231 can be, but not limited to, a complex value such that the equalized signals S₁-S₂₅₆ can be rotated precisely to become in phase.

In this case, the equalizer 231 can be performed by the narrow band equalizer, as illustrated in FIG. 1C. The narrow band equalizer 231 can provide phase and amplitude modifications to each of the signals W₁-W₂₅₆ featuring a constant phase shift and constant amplitude attenuation across a narrow frequency band. Alternatively, the equalizer 231 can be performed by the broadband equalizer, as illustrated in FIG. 1C. The broadband equalizer 231 can provide phase and amplitude modifications to each of the signals W₁-W₂₅₆ featuring a constant phase shift and a constant amplitude attenuation in each sub-band across a broad frequency band, but the phase shift and amplitude attenuation in one sub-band across the broad frequency band is different from those in the other sub-bands across the broad frequency band.

Next, the equalized digital signals S₁-S₂₅₆ are transmitted in parallel to the wave-front demultiplexer 232 through, e.g., two-hundred-and-fifty-six parallel signal paths or channels between the output ports of the equalizer 231 and the input ports of the wave-front demultiplexer 232.

Referring to FIG. 5E, upon receiving, in parallel, the equalized digital signals S₁-S₂₅₆ output in parallel from the equalizer 531, the wave-front demultiplexer 232 extracts two-hundred-and-fifty-six coherently combined digital signals Z₁-Z₂₅₆, which are substantially equal to the digital signals X₁-X₂₅₆ respectively or to the digital signals X₁-X₂₅₆ multiplied by the same scalar, from the digital signals S₁-S₂₅₆ by performing the above-mentioned wave-front demultiplexing transformation and outputs the digital signals Z₁-Z₂₅₆ in parallel, which can be referred to as the description illustrated in FIG. 1E. In this case, as illustrated in FIG. 1E, the number of I is equal to 256. The wave-front demultiplexer 232 may include 256*256 computing units and 256 summing processors. The computing units form a processor array with 256 rows and 256 columns. The input signals S₁-S₂₅₆ can be received by the computing units in the respective 256 columns in the processor array. Upon receiving the input signals S₁-S₂₅₆, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The 256 summing processors can output the four signals Z₁-Z₂₅₆ each combined with the weighted signals output from the computing units in a corresponding one of the 256 rows in the processor array. The digital signals Z₁-Z₂₅₆ can be, but not limited to, IF digital signals or RF digital signals. Each of the digital signals Z₁-Z₂₅₆ is a linear combination, i.e. weighted sum, each summed with the digital signals S₁-S₂₅₆ multiplied by respective weightings, and distributions of the weightings of any two input components in all digital signals Z₁-Z₂₅₆ are orthogonal, which can be referred to as the description illustrated in FIG. 1E.

The wave-front demultiplexer 232 can be, but not limited to, embedded in a processor. The wave-front demultiplexer 232 can be hardware achieving the wave-front demultiplexing transform, such as IFFT chip, 256-by-256 Butler matrix, or a device performing inverse Fourier transformation, inverse discrete Fourier transformation, inverse Hartley transformation, Hadamard transformation, any other inverse Fourier-related transformation, or any transformation of a 256-by-256 orthogonal matrix. Alternatively, the function of the wave-front demultiplexer 232 can be realized by software installed in and performed by the processor, wherein the software can perform the above wave-front demultiplexing transformation.

The flow chart of the optimizing and equalizing process shown in FIG. 1C can be applied to the embodiment illustrated in FIG. 5E. For example, the optimizer 235 receives the signals Z₂₅₁-Z₂₅₆ output from the wave-front demultiplexer 232 and outputs the control signal CS to the equalizer 231 so as to adjust the respective weightings of the equalizer 231 when the optimizing and equalizing process is performed.

The equalizer 231, the wave-front demultiplexer 232 and the optimizer 235 can be, but not limited to, embedded in a module or processor 230. The module or processor 230 may include one or more integrated circuit chips, one or more system-on chips, or one or more chip packages. The equalizer 231 can be hardware or can be realized by software installed in and performed by the processor 230. The optimizer 235 can be hardware or can be realized by software installed in and performed by the processor 230.

Next, the 250-to-1 time-domain multiplexer 540 combines or integrates the two-hundred-and-fifty input signals Z₁-Z₂₅₀, each having a frequency bandwidth of J/250 sampled at a sampling rate of K/250, into an output signal B₁, having a frequency bandwidth of J sampled at a sampling rate of K, with high data flow rate. Thereby, the output signal B₁ is substantially equal to the input signal A₁. As a result, the input signal A₁ will be fully recovered. The input signals Z₁-Z₂₅₀ are substantially equal to the input signals X₁-X₂₅₀, respectively. The input signals Z₁-Z₂₅₀ are substantially equal to the input signals X₁-X₂₅₀, respectively, or to the signals X₁-X₂₅₀ multiplied by the same scalar, respectively.

Referring to FIG. 5F, the system 500 shown in FIG. 5F is similar to the system 500 illustrated in FIG. 5E except that the system 500 illustrated in FIG. 5F further includes a 1-to-50 time-domain demultiplexer 538 a, a 1-to-170 time-domain demultiplexer 538 b, a 1-to-30 time-domain demultiplexer 538 c, a 50-to-1 time-domain multiplexer 540 a, a 170-to-1 time-domain multiplexer 540 b, and a 30-to-1 time-domain multiplexer 540 c.

The 1-to-50 time-domain demultiplexer 538 a includes an input port and 50 output ports and can divide an input signal A₁ from the input port to 50 parallel outputs signals X₁-X₅₀, respectively output from its 50 output ports, sequentially in time. The TDDM 538 b includes an input port and 170 output ports and can divide an input signal A₂ from the input port to 170 parallel outputs signals X₅₁-X₂₂₀, respectively output from its 170 output ports, sequentially in time. The TDDM 538 c includes an input port and 30 output ports and can divide an input signal A₃ from the input port to 30 parallel outputs signals X₂₂₁-X₂₅₀, respectively output from its 30 output ports, sequentially in time. Each of the X₂₅₁-X₂₅₆ is a stream of pilot codes input to the wave-front multiplexer 213.

The TDDM 538 a can divide an input digital signal A₁ having a frequency bandwidth of J sampled at a sampling rate of K into 50 output digital signals X₁-X₅₀, each having a frequency bandwidth of J/50 sampled at a sampling rate of K/50, passing through 50 parallel signal paths, such as physical or wireless channels, coupled to the wave-front multiplexer 213. The TDDM 538 b can divide an input digital signal A₂ having a frequency bandwidth of J sampled at a sampling rate of K into 170 output digital signals X₅₁-X₂₂₀, each having a frequency bandwidth of J/170 sampled at a sampling rate of K/170, passing through 170 parallel signal paths, such as physical or wireless channels, coupled to the wave-front multiplexer 213. The TDDM 538 c can divide an input digital signal A₂ having a frequency bandwidth of J sampled at a sampling rate of K into 30 output digital signals X₂₂₁-X₂₅₀, each having a frequency bandwidth of J/30 sampled at a sampling rate of K/30, passing through 30 parallel signal paths, such as physical or wireless channels, coupled to the wave-front multiplexer 213.

Next, the signals X₁-X₂₅₆ are processed to be output as the signals Z₁-Z₂₅₆, which can be referred to as the description illustrated in FIG. 5E.

The 50-to-1 TDM 540 a can integrate multiple input signals Z₁-Z₅₀, each having a frequency bandwidth of J/50 sampled at a sampling rate of K/50, passing through 50 parallel signal paths, such as physical or wireless channels, coupled to the wave-front demultiplexer 232 into an output signal B₁ having a frequency bandwidth of J sampled at a sampling rate of K. The 170-to-1 TDM 540 b can integrate multiple input signals Z₅₁-Z₂₂₀, each having a frequency bandwidth of J/170 sampled at a sampling rate of K/170, passing through 170 parallel signal paths, such as physical or wireless channels, coupled to the wave-front demultiplexer 232 into an output signal B₂ having a frequency bandwidth of J sampled at a sampling rate of K. The 30-to-1 TDM 540 c can integrate multiple input signals Z₂₂₁-Z₂₅₀, each having a frequency bandwidth of J/30 sampled at a sampling rate of K/30, passing through 30 parallel signal paths, such as physical or wireless channels, coupled to the wave-front demultiplexer 232 into an output signal B₃ having a frequency bandwidth of J sampled at a sampling rate of K.

The output signal B₁ is reconstituted by combining the 50 recovered signals Z₁-Z₅₀ into one with high data flow rate through a TDM 540 a. The output signal B₁ is substantially equaled to the input signal A₁. As a result, the input signal A₁ will be fully recovered. The output signal B₂ is reconstituted by combining the 170 recovered signals Z₅₁-Z₂₂₀ into one with high data flow rate through a TDM 540 b. The output signal B₂ is substantially equaled to the input signal A₂. As a result, the input signal A₂ will be fully recovered. The output signal B₃ is reconstituted by combining the 30 recovered signals Z₂₂₁-Z₂₅₀ into one with high data flow rate through a TDM 540 b. The output signal B₃ is substantially equaled to the input signal A₃. As a result, the input signal A₃ will be fully recovered.

Referring to FIG. 5G and FIG. 5H, the system 500 is for a multipoint-to-point design, but the system 500 shown in FIG. 5G and FIG. 5H are still similar to the system 500 illustrated in FIG. 5F except that the system 500 illustrated in FIG. 5G and FIG. 5H uses the number Nt of signal transmitting sources, such as including a first transmitting source L₁ processing two, i.e. A₁ and A₃ of the digital signals A₁, A₂ and A₃, and a second transmitting source L₂ processing one, i.e. A₂, of the digital signals A₁, A₂ and A₃, and the number Nr of signal receiving sources, such as such as including only one receiving source outputting the three digital signals B₁, B₂ and B₃ substantially equal to the digital signals A₁, A₂ and A₃ respectively or to the digital signals A₁, A₂ and A₃ multiplied by the same scalar, respectively, wherein the number of Nt could be any number equal to or greater than 2, 3, 4, 5, 6, 7, 8, 9 or 10, and could be greater than the number of Nr that could be one in this embodiment. The number Nt of the transmitting sources have the same wave-front multiplexer as one another or each other and use different input ports in sequence for receiving different extraneous signals. Referring to FIG. 5H, a method for processing signals or data streams by using the system 500 shown in Fig. FIG. 5G and FIG. 5H is described below.

In the source L₁, an extraneous digital signal A₁ is transmitted to a 1-to-50 TDDM 538 a through, e.g., a signal path, a wireless channel or a physical channel, and an extraneous digital signal A₃ is transmitted to a 1-to-30 TDDM 538 c through, e.g., a signal path, a wireless channel or a physical channel. The signal A₃ could be independent from the signal A₁. There are one-hundred-and-seventy ground signals X₅₁-X₂₂₀ couple to the wave-front multiplexer 213 a that are represented no signals input to one-hundred-and-seventy input ports of the wave-front multiplexer 213 a. Six pilot or diagnostic signals X_(251a)-X_(256a) are transmitted to six input ports of the wave-front multiplexer 213 a. Each of the pilot or diagnostic signals X_(251a)-X_(256a) may have a single frequency and fixed amplitude. Alternatively, the pilot or diagnostic signals X_(251a)-X_(256a) could change based on time or could be any signal known by the system 500. The two signals A₁ and A₃ are unknown by the system 500 and input into the system 500 from one or more extraneous systems.

The TDDM 538 a includes an input port and 50 output ports and can divide an extraneous digital signal A₁ from the input port to 50 parallel outputs signals X_(1a)-X_(50a), respectively output from its 50 output ports, sequentially in time, wherein the 1-to-50 TDDM 538 a can divide an input digital signal A₁ having a frequency bandwidth of J sampled at a sampling rate of K into 50 output digital signals X_(1a)-X_(50a), each having a frequency bandwidth of J/50 sampled at a sampling rate of K/50, passing through 50 parallel signal paths, such as physical or wireless channels, coupled to the wave-front multiplexer 213 a.

The TDDM 538 c includes an input port and 30 output ports and can divide an extraneous digital signal A₃ from the input port to 30 parallel outputs signals X_(221a)-X_(250a), respectively output from its 30 output ports, sequentially in time, wherein the 1-to-30 TDDM 538 c can divide an input digital signal A₃ having a frequency bandwidth of J sampled at a sampling rate of K into 30 output digital signals X_(221a)-X_(250a), each having a frequency bandwidth of J/30 sampled at a sampling rate of K/30, passing through 30 parallel signal paths, such as physical or wireless channels, coupled to the wave-front multiplexer 213 a.

Next, the wave-front multiplexer 213 a performs the above-mentioned wave-front multiplexing transformation to process the signals X_(1a)-X_(50a), X₅₁-X₂₂₀ and X_(221a)-X_(256a) into multiple linear combinations, each combined with the signals X_(1a)-X_(50a), X₅₁-X₂₂₀ and X_(221a)-X_(256a) multiplied by respective weightings, represented by 256 digital signals Y_(1a)-Y_(256a). Next, the wave-front multiplexer 213 a outputs the signals Y_(1a)-Y_(256a) from its output ports of the wave-front multiplexer 213 a.

Next, each of eight 32-to-1 TDM 542 can integrate 32 input signals form wave-front multiplexer 213 a, each having a frequency bandwidth of J/32 sampled at a sampling rate of K/32, passing through 32 parallel signal paths, such as physical or wireless channels, coupled to the wave-front multiplexer 213 a into an output signal G having a frequency bandwidth of J sampled at a sampling rate of K. For example, the 1^(st) 32-to-1 TDM 542 a 1 can integrate input signals Y_(1a)-Y_(32a) into an output signal G_(1a), the 2^(nd) TDM 542 b 1 can integrate input signals Y_(33a)-Y_(64a) into an output signal G_(2a), the 3^(rd) TDM 542 c 1 can integrate input signals Y_(65a)Y_(96a) into an output signal G_(3a), the 4^(th) TDM 542 d 1 can integrate input signals Y_(97a)-Y_(128a) into an output signal G_(4a), the 5^(th) TDM 542 e 1 can integrate input signals Y_(129a)-Y_(160a) into an output signal G_(5a), the 6^(th) TDM 542 f 1 can integrate input signals Y_(161a)-Y_(192a) into an output signal G_(6a), the 7^(th) TDM 542 g 1 can integrate input signals Y_(193a)-Y_(224a) into an output signal G_(7a), the 8^(th) TDM 542 h 1 can integrate input signals Y_(225a)-Y_(256a) into an output signal G_(8a). The six TDM 542 b 1-TDM 542 g 1 are not shown in FIG. 5H.

Next, the eight 32-to-1 TDM 542 a 1-TDM 542 h 1 outputs the digital signals G_(1a)-G_(8a) from the output ports of TDM 542 a 1-TDM 542 h 1, and the digital signals G_(1a)-G_(8a) are respectively transmitted into eight input ports of the optical transmit devices 520 a 1-520 h 1 through, e.g., eight parallel channels, such as wireless channels or physical channels. Each of the optical transmit devices or transmitters 520 a 1-520 h 1 can be a laser generator, wherein the laser generator can emit a distributed feedback laser (DFB laser), a Fabry-perot laser (F-P laser) or a vertical cavity surface emitting laser (VCSEL) to the mode-group diversity multiplexing (MGDM) device 516 a.

Next, the optical transmit devices 520 a 1-520 h 1 emit 8 individual optical signals T_(1a)-T_(8a) based on the digital signals G_(1a)-G_(8a) to the MGDM device 516 a, wherein the optical signal T_(1a) carries information associated with the digital signal G_(1a), the optical signal T_(2a) carries information associated with the digital signal G_(2a), the optical signal T_(3a) carries information associated with the digital signal G_(3a), the optical signal T_(4a) carries information associated with the digital signal G_(4a), the optical signal T_(5a) carries information associated with the digital signal G_(5a), the optical signal T_(6a) carries information associated with the digital signal G_(6a), the optical signal T_(7a) carries information associated with the digital signal G_(7a), and the optical signal T_(8a) carries information associated with the digital signal G_(8a).

The MGDM device 516 a has been proposed as a way of creating parallel communication channels over the multimode fiber (MMF) 524. The MGDM 516 a has been proved as an efficient scheme to overcome the limited bandwidth of the multimode fiber (MMF) 524. MGDM device 516 a can multiplex the optical signals T_(1a)-T_(8a) into different mode groups of light, propagating with different angles in the MMF 524, wherein each mode groups of the light are used to carry different information so that the data throughput is increased without having additional bandwidth. The four optical transmit devices 520 c 1-520 f 1, signals G_(2a)-G_(7a), and T_(2a)-T_(7a) are not shown in FIG. 5H.

In the source L₂, an extraneous digital signal A₂ is transmitted to an input port of a 1-to-170 TDDM 538 b through, e.g., a signal path, a wireless channel or a physical channel. There are eighty ground signals X_(1b)-X_(50b) and X_(221b)-X_(250b) couple to the wave-front multiplexer 213 b that are represented no signals input to eighty input ports of the wave-front multiplexer 213 b. Sixth pilot or diagnostic signals X_(251b)-X_(256b) are transmitted to six input ports of the wave-front multiplexer 213 b. Each of the pilot or diagnostic signals X_(251b)-X_(256b) may have a single frequency and fixed amplitude. Alternatively, the six signals X_(251b)-X_(256b) could change based on time or could be any signal known by the system 500. The extraneous digital signal A₂ is unknown by the system 500 and input into the system 500 from an extraneous system. The six pilot or diagnostic signals X_(251b)-X_(256b) of the source L₂ are the same as the pilot or diagnostic signal X_(251a)-X_(256a) of the source L₁, respectively.

The TDDM 538 b includes an input port and 170 output ports and can divide an extraneous digital signal A₂ from the input port to 170 parallel outputs signals X_(51b)-X_(220b), respectively output from its 170 output ports, sequentially in time, wherein the 1-to-170 TDDM 538 b can divide an input digital signal A₂ having a frequency bandwidth of J sampled at a sampling rate of K into 170 output digital signals X_(51b)-X_(220b), each having a frequency bandwidth of J/170 sampled at a sampling rate of K/170, passing through 170 parallel signal paths, such as physical or wireless channels, coupled to the wave-front multiplexer 213 b.

Next, the wave-front multiplexer 213 b performs the above-mentioned wave-front multiplexing transformation to process the signals X_(1b)-X_(50b), X_(51b)-X_(220b), X_(221b)-X_(250b) and X_(251b)-X_(256b) into multiple linear combinations, each combined with the signals X_(51b)-X_(220b) multiplied by respective weightings, represented by 256 digital signals Y_(1b)-Y_(256b).

Next, each of eight 32-to-1 TDM 542 can integrate 32 input signals form wave-front multiplexer 213 b, each having a frequency bandwidth of J/32 sampled at a sampling rate of K/32, passing through 32 parallel signal paths, such as physical or wireless channels, coupled to the wave-front multiplexer 213 b into an output signal G having a frequency bandwidth of J sampled at a sampling rate of K. For example, the 1^(st) 32-to-1 TDM 542 a 2 can integrate input signals Y_(1b)-Y_(32b) into an output signal G_(1b), the 2^(nd) TDM 542 b 2 can integrate input signals Y_(33b)-Y_(64b) into an output signal G_(2b), the 3^(rd) TDM 542 c 2 can integrate input signals Y_(65b)-Y_(96b) into an output signal G_(3b), the 4^(th) TDM 542 d 2 can integrate input signals Y_(97b)-Y_(128b) into an output signal G₀, the 5^(th) TDM 542 e 2 can integrate input signals Y_(129b)-Y_(160b) into an output signal G_(5b), the 6^(th) TDM 542 f 2 can integrate input signals Y_(161b)-Y_(192b) into an output signal G_(6b), the 7^(th) TDM 542 g 2 can integrate input signals Y_(193b)-Y_(224b) into an output signal G_(7b), the 8^(th) TDM 542 h 2 can integrate input signals Y_(225b)-Y_(256b) into an output signal G_(8b). The six TDM 542 b 2-TDM 542 g 2 are not shown in FIG. 5H.

Next, the eight 32-to-1 TDM 542 a 2-TDM 542 h 2 outputs the digital signals G_(1b)-G_(8b) from the output ports of TDM 542 a 2-TDM 542 h 2, and the digital signals G_(1b)-G_(8b) are respectively transmitted into eight input ports of the optical transmit devices 520 _(a2)-520 _(h2) through, e.g., eight parallel channels, such as wireless channels or physical channels. Each of the optical transmit devices or transmitters 520 _(a2)-520 _(h2) can be a laser generator, wherein the laser generator can emit a distributed feedback laser (DFB laser), a Fabry-perot laser (F-P laser) or a vertical cavity surface emitting laser (VCSEL) to the mode-group diversity multiplexing (MGDM) device 516 b.

Next, the optical transmit devices 520 _(a2)-520 _(h2) emit 8 individual optical signals T_(1b)-T_(8b) based on the digital signals G_(1b)-G_(8b) to the MGDM device 516 b, wherein the optical signal T_(1b) carries information associated with the digital signal G_(1b), the optical signal T_(2b) carries information associated with the digital signal G_(2b), the optical signal T_(3b) carries information associated with the digital signal G_(3b), the optical signal T_(4b) carries information associated with the digital signal G_(4b), the optical signal T_(5b) carries information associated with the digital signal G_(5b), the optical signal T_(6b) carries information associated with the digital signal G_(6b), the optical signal T_(7b) carries information associated with the digital signal G_(7b), and the optical signal T_(8b) carries information associated with the digital signal G_(8b).

The MGDM device 516 b has been proposed as a way of creating parallel communication channels over the multimode fiber (MMF) 524. The MGDM 516 a has been proved as an efficient scheme to overcome the limited bandwidth of the multimode fiber (MMF) 524. MGDM device 516 b can multiplex the optical signals T_(1b)-T_(8b) into different mode groups of light, propagating with different angles in the MMF 524, wherein each mode groups of the light are used to carry different information so that the data throughput is increased without having additional bandwidth. The optical transmit devices 520 c 2-520 f 2, signals G_(2b)-G_(7b) and T_(2b)-T_(7b) are not shown in FIG. 5H.

Referring to FIG. 5G, upon receiving the different mode groups of the light output from the MGDM device 516 a, MGDM device 516 b and propagating over the MMF 524, the mode-group diversity demultiplexing (MGDDM) device 518 demultiplexes the different mode groups of the light based on the time when the different mode groups of the light approach the MGDDM device 518 and on the angles of the different mode groups of the light into multiple optical signals V₁-V₈ received by the optical detectors 522 a-522 g and 522 _(h). Upon respectively receiving the 8 optical signals V₁-V₈ output in parallel from the MGDDM device 518 respectively, the 8 optical detectors 522 a-522 h can send 8 digital signals H₁-H₈ to the to eight 1-to-32 TDDM 544 a-TDDM 544 h, respectively. The digital signal H₁ carries information associated with the optical signal V₁, the digital signal H₂ carries information associated with the optical signal V₂, the digital signal H₃ carries information associated with the optical signal V₃, the digital signal H₄ carries information associated with the optical signal V₄, the digital signal H₅ carries information associated with the optical signal V₅, the digital signal H₆ carries information associated with the optical signal V₆, the digital signal H₇ carries information associated with the optical signal V₇ and the digital signal Hg carries information associated with the optical signal V₈. The six TDDM 544 b-TDDM 544 g and the signals V₂-V₇ and signals H₂-H₇ are not shown in FIG. 5G.

Next, the 1-to-32 TDDM 544 a can divide an input digital signal H₁ having a frequency bandwidth of J sampled at a sampling rate of K into 32 output digital signals W₁-W₃₂, each having a frequency bandwidth of J/32 sampled at a sampling rate of K/32, passing through 32 parallel signal paths, such as physical or wireless channels, coupled to the Equalizer 231. The 1-to-32 TDDM 544 b can divide an input digital signal H₂ having a frequency bandwidth of J sampled at a sampling rate of K into 32 output digital signals W₃₃-W₆₄, each having a frequency bandwidth of J/32 sampled at a sampling rate of K/32, passing through 32 parallel signal paths, such as physical or wireless channels, coupled to the Equalizer 231. The 1-to-32 TDDM 544 c can divide an input digital signal H₃ having a frequency bandwidth of J sampled at a sampling rate of K into 32 output digital signals W₆₅-W₉₆, each having a frequency bandwidth of J/32 sampled at a sampling rate of K/32, passing through 32 parallel signal paths, such as physical or wireless channels, coupled to the Equalizer 231. The 1-to-32 TDDM 544 d can divide an input digital signal H₄ having a frequency bandwidth of J sampled at a sampling rate of K into 32 output digital signals W₉₇-W₁₂₈, each having a frequency bandwidth of J/32 sampled at a sampling rate of K/32, passing through 32 parallel signal paths, such as physical or wireless channels, coupled to the Equalizer 231. The 1-to-32 TDDM 544 e can divide an input digital signal H₅ having a frequency bandwidth of J sampled at a sampling rate of K into 32 output digital signals W₁₂₉-W₁₆₀, each having a frequency bandwidth of J/32 sampled at a sampling rate of K/32, passing through 32 parallel signal paths, such as physical or wireless channels, coupled to the Equalizer 231. The 1-to-32 TDDM 544 f can divide an input digital signal H₆ having a frequency bandwidth of J sampled at a sampling rate of K into 32 output digital signals W₁₆₁-W₁₉₂, each having a frequency bandwidth of J/32 sampled at a sampling rate of K/32, passing through 32 parallel signal paths, such as physical or wireless channels, coupled to the Equalizer 231. The 1-to-32 TDDM 544 g can divide an input digital signal H₇ having a frequency bandwidth of J sampled at a sampling rate of K into 32 output digital signals W₁₉₃-W₂₂₄, each having a frequency bandwidth of J/32 sampled at a sampling rate of K/32, passing through 32 parallel signal paths, such as physical or wireless channels, coupled to the Equalizer 231. The 1-to-32 TDDM 544 h can divide an input digital signal Hg having a frequency bandwidth of J sampled at a sampling rate of K into 32 output digital signals W₂₂₅-W₂₅₆, each having a frequency bandwidth of J/32 sampled at a sampling rate of K/32, passing through 32 parallel signal paths, such as physical or wireless channels, coupled to the Equalizer 231.

Next, referring to FIG. 5E, the digital signals W₁-W₂₅₆ are transmitted in parallel into 256 input ports of the equalizer 231 through, e.g., 256 parallel channels, such as wireless channels or physical channels. The input ports of the equalizer 231 are arranged in parallel for receiving the digital signals W₁-W₂₅₆, respectively. After the digital signals W₁-W₂₅₆ are transmitted in parallel into the equalizer 231, the above optimizing and equalizing process, as illustrated in FIG. 1C, is performed such that the digital signals W₁-W₂₅₆ can be compensated to be multiplied by four respective weightings by the equalizer 231, wherein the 256 respective weightings of the equalizer 231 can be adjusted based on a control signal CS, output from the optimizer 235 and input into the equalizer 231. The optimizing and equalizing process can be referred to as the optimizing and equalizing process as illustrated in FIG. 1C. After the optimizing and equalizing process, the equalizer 231 outputs four equalized digital signals S₁-S₂₅₆, respectively, from its output ports of the equalizer 231. Each of the equalized digital signals S₁-S₂₅₆ is created by the equalizer 231 multiplying the corresponding one of the digital signals W₁-W₂₅₆ by a weighting of the equalizer 231. For example, the equalized digital signal S₁ is created by the equalizer 231 multiplying the digital signal W₁ by a weighting of the equalizer 231.

Next, the equalized digital signals S₁-S₂₅₆ are transmitted in parallel into input ports of the wave-front demultiplexer 232 through 256 parallel signal paths between the output ports of the equalizer 231 and the input ports of the wave-front demultiplexer 232. Each of the 256 respective weightings of the equalizer 231 can be, but not limited to, a complex value such that the equalized signals S₁-S₂₅₆ can be rotated precisely to become in phase. In this case, the equalizer 231 can be performed by the narrow band equalizer, as illustrated in FIG. 1C. The narrow band equalizer 231 can provide phase and amplitude modifications to each of the signals W₁-W₂₅₆ featuring a constant phase shift and constant amplitude attenuation across a narrow frequency band. Alternatively, the equalizer 231 can be performed by the broadband equalizer, as illustrated in FIG. 1C. The broadband equalizer 231 can provide phase and amplitude modifications to each of the signals W₁-W₂₅₆ featuring a constant phase shift and a constant amplitude attenuation in each sub-band across a broad frequency band, but the phase shift and amplitude attenuation in one sub-band across the broad frequency band is different from those in the other sub-bands across the broad frequency band.

Referring to FIG. 5G, upon receiving, in parallel, the equalized digital signals S₁-S₂₅₆ output in parallel from the equalizer 531, the wave-front demultiplexer 232 extracts two-hundred-and-fifty-six coherently combined digital signals Z₁-Z₂₅₆, which are substantially equal to the digital signals X₁-X₂₅₆ respectively or to the digital signals X₁-X₂₅₆ multiplied by the same scalar, respectively, from the digital signals S₁-S₂₅₆ by the above-mentioned wave-front demultiplexing transform, and outputs the digital signals Z₁-Z₂₅₆ in parallel, which can be referred to as the description illustrated in FIG. 1E. In this case, as illustrated in FIG. 1E, the number of I is equal to 256. The wave-front demultiplexer 232 has 256*256 computing units and 256 summing processors. The computing units form a processor array with four rows and 256 columns. The input signals S₁-S₂₅₆ can be received by the computing units in the respective four columns in the processor array. Upon receiving the input signals S₁-S₂₅₆, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The 256 summing processors can output the four signals Z₁-Z₂₅₆ each combined with the weighted signals output from the computing units in a corresponding one of the 256 rows in the processor array. The digital signals Z₁-Z₂₅₆ can be, but not limited to, four IF digital signals or four RF digital signals. Each of the digital signals Z₁-Z₂₅₆ is a linear combination, i.e. weighted sum, each summed with the digital signals S₁-S₂₅₆ multiplied by respective weightings, and distributions of the weightings of any two input components in all digital signals Z₁-Z₂₅₆ are orthogonal, which can be referred to as the description illustrated in FIG. 1E.

The wave-front demultiplexer 232 can be, but not limited to, embedded in a processor. The wave-front demultiplexer 232 can be hardware achieving the wave-front demultiplexing transform, such as IFFT chip, a component for 256-by-256 inverse Butler matrix, or a device performing inverse Fourier transformation, inverse discrete Fourier transformation, inverse Hartley transformation, Hadamard transformation, any other inverse Fourier-related transformation, or any transformation of a 256-by-256 orthogonal matrix. Alternatively, the function of the wave-front demultiplexer 232 can be realized by software installed in and performed by the processor, wherein the software can perform the above wave-front demultiplexing transform.

The optimizer 235 can be in a signal path between the output ports of wave-front demultiplexer 232 and the equalizer 231. The flow chart of the optimizing and equalizing process shown in FIG. 1C can be applied to the embodiment illustrated in FIG. 5E. For example, the optimizer 235 can receive the signals Z₂₅₁-Z₂₅₆ output from the wave-front demultiplexer 232 and outputs the control signal CS to the equalizer 231 so as to adjust the four respective weightings of the equalizer 231 when the optimizing and equalizing process is performed.

The equalizer 231, the wave-front demultiplexer 232 and the optimizer 235 can be, but not limited to, embedded in a processor 230, such as single integrated circuit chip or single chip package. The equalizer 231 can be hardware or can be realized by software installed in and performed by the processor 230. The optimizer 235 can be hardware or can be realized by software installed in and performed by the processor 230.

After the equalized digital signals S₁-S₂₅₆ are input in parallel to the wave-front demultiplexer 232, the wave-front demultiplexer 232 performs the above-mentioned wave-front demultiplexing transformation to process the equalized digital signals S₁-S₂₅₆ into two-hundred-and-fifty-six linear combinations, each combined with the equalized digital signals S₁-S₂₅₆ multiplied by respective weightings, represented by the two-hundred-and-fifty-six digital signals Z₁-Z₂₅₆ output in parallel from the four parallel output ports of the wave-front demultiplexer 232. The digital signals Z₁-Z₂₅₆ are substantially equaled to the digital signals X₁-X₂₅₆, respectively.

Next, the 50-to-1 TDM 540 a can integrate 50 input signals Z₁-Z₅₀, each having a frequency bandwidth of J/50 sampled at a sampling rate of K/50, passing through 50 parallel signal paths, such as physical or wireless channels, coupled to the wave-front demultiplexer 232 into an output signal B₁ having a frequency bandwidth of J sampled at a sampling rate of K.

The output signal B₁ is reconstituted by combining the 50 recovered signals Z₁-Z₅₀ into one with high data flow rate through a TDM 540 a. The output signal B₁ is substantially equaled to the input signal A₁. As a result, the input signal A₁ will be fully recovered.

Next, the 170-to-1 TDM 540 b can integrate multiple input signals Z₅₁-Z₂₂₀, each having a frequency bandwidth of J/170 sampled at a sampling rate of K/170, passing through 170 parallel signal paths, such as physical or wireless channels, coupled to the wave-front demultiplexer 232 into an output signal B₂ having a frequency bandwidth of J sampled at a sampling rate of K.

The output signal B₂ is reconstituted by combining the 170 recovered signals Z₅₁-Z₂₂₀ into one with high data flow rate through a TDM 540 b. The output signal B₂ is substantially equaled to the input signal A₂. As a result, the input signal A₂ will be fully recovered.

Next, the 30-to-1 TDM 540 c can integrate multiple input signals Z₂₂₁-Z₂₅₀, each having a frequency bandwidth of J/30 sampled at a sampling rate of K/30, passing through 30 parallel signal paths, such as physical or wireless channels, coupled to the wave-front demultiplexer 232 into an output signal B₃ having a frequency bandwidth of J sampled at a sampling rate of K.

The output signal B₃ is reconstituted by combining the 30 recovered signals Z₂₂₁-Z₂₅₀ into one with high data flow rate through a TDM 540 c. The output signal B₃ is substantially equaled to the input signal A₃. As a result, the input signal A₃ will be fully recovered.

Fifth Embodiment: Application to Secured Satcom or Satellite Communication

FIG. 6A shows architecture as Satcom waveforms or signals spread through the number N of signal-channel-per-carrier (SCPC) channels with the same polarization in narrowband frequency slots over a satellite. The system 600 features point-to-point communications. A system 600 at a transmitting side, i.e. an uplink ground terminal 605, includes a 1-to-M time domain demultiplexer (TDDM) 604 for dividing an input signal A₀ having a high bandwidth sampled at a high sampling rate into multiple output signals X₁-X_(M) each having a low bandwidth sampled at a low sampling rate, the above-mentioned wave-front multiplexer 213, arranged as outputs of the 1-to-M time domain demultiplexer (TDDM) 604, for performing the above-mentioned wave-front multiplexing transform to X₁-X_(N), the number N of frequency up-conversion components 601, arranged in parallel and at outputs of the wave-front multiplexer 213, for converting the number N of signals Y₁-Y_(N) output from the wave-front multiplexer 213 into the number N of signals U₁-U_(N) each having or modulating a distinct carrier within a distinct frequency sub-band for satellite communication from any other one of the number N of signals U₁-U_(N), wherein the frequency sub-bands of the signals U₁-U_(N) are not overlapped to one another or each other, an output multiplexer (O-Mux) 602, arranged at outputs of the frequency up-conversion components 601, that could be a frequency division multiplexer (FDM) for combining the number N of signals U₁-U_(N) into a signal composite signal P₀, and an antenna array 603, arranged at an output of the output multiplexer 602, for receiving the signal P₀ output from the output multiplexer 602 and outputting or broadcasting a microwave signal Q₀ to a satellite 650, wherein the microwave signal Q₀ carries information associated with the signal P₀.

Referring to FIG. 6A, the system 600 at a receiving side, i.e. a downlink ground terminal 606, includes an antenna array 607 for receiving or intercepting a microwave signal R₀ from the satellite 608, wherein the microwave signal R₀ carries information associated with the microwave signal Q₀, an input multiplexer (I-Mux) 608, arranged at an output of the antenna array 607, for receiving a microwave signal K₀ output from the antenna array 607, wherein the microwave signal R₀ carries information associated with the signal K₀, wherein the input multiplexer 608 can be a frequency division demultiplexer (FDDM) adapted to divide the signal K₀ into the number N of signals wherein each of the signals I₁-I_(N) has or modulates a distinct carrier within a distinct frequency sub-band from any other one of the number N of signals wherein the frequency sub-bands of the signals I₁-I_(N) are not overlapped to one another or each other, the number N of frequency down-conversion components 609, arranged in parallel and at outputs of the input multiplexer 608, for converting the number N of signals I₁-I_(N) output from the input multiplexer 608 into the number N of signals W₁-W_(N), the above-mentioned equalizer 231, arranged at outputs of the frequency down-conversion components 609, for compensating the number N of signals W₁-W_(N) each to be multiplied by respective weightings so as to output the number N of equalized signals S₁-S_(N), the above-mentioned optimizer 235, arranged at one or more inputs of the frequency down-conversion components 609, for adjusting the respective weightings of the equalizer 231, the above-mentioned wave-front demultiplexer 232, arranged at outputs of the equalizer 231 and at one or more inputs of the optimizer 235, for performing the above-mentioned wave-front demultiplexing transform to the equalized signals S₁-S_(N), the signal P₀ output from the output multiplexer 602, and a M-to-1 time-domain multiplexer 610, arranged at outputs of the wave-front demultiplexer 232, for combining or integrating the number M of signals Z₁-Z_(M), each having a low frequency bandwidth sampled at a low sampling rate, into an output signal B₀ having a high frequency bandwidth sampled at a high sampling rate.

In this case as above illustrated in FIG. 6A, the number of N is an integer that could be any number equal to or greater than 2, 4, 8, 16, 32, 64, 128 or 256. The number of M is an integer that could be any number less than the number of N.

Referring to FIG. 6A, a method for processing data streams is described as blow. The 1-to-M TDDM 604 includes an input port receiving a digital or analog signal A₀ and the number M of output ports outputting the number M of digital or analog signals X₁-X_(M). A TDDM is defined herein to divide an input signal having a high bandwidth sampled at a high sampling rate into multiple output signals each having a low bandwidth sampled at a low sampling rate. For example, in this embodiment, the 1-to-M TDDM 604 can divide the input signal A₀ having a frequency bandwidth of J sampled at a sampling rate of K into the number M of the output signals X₁-X_(M), each having a frequency bandwidth of J/M sampled at a sampling rate of K/M, passing through the number M of parallel signal paths, such as physical or wireless channels, coupled to the wave-front multiplexer 213.

Next, referring to FIG. 6A, the digital or analog signals X₁-X_(M) output from the 1-to-M time-domain demultiplexer 604 and one or more pilot or diagnostic signals X_(M+1)-X_(N) that can analog or digital ones can be transmitted to the wavefront multiplexer 213. Each of the pilot or diagnostic signals X_(M+1)-X_(N) may be a pilot or diagnostic signal that may have a single frequency and fixed amplitude. Alternatively, the pilot or diagnostic signals X_(M+1)-X_(N) could change based on time or could be any signal known by the system 600. The extraneous signal A₀ divided into the number M of the digital or analog signals X₁-X_(M) by the 1-to-M time-domain demultiplexer 604 is unknown by the system 600 and input into the system 600 from an extraneous system.

Next, referring to FIG. 6A, upon receiving, in parallel, the number M of the individual and independent digital signals X₁-X_(M) and the number N−M of pilot or diagnostic signals X_(M+1)-X_(N), the wave-front multiplexer 213 can processes the number N of the analog or digital signals X₁-X_(N) into the number N of analog or digital signals Y₁-Y_(N) by the above-mentioned wave-front multiplexing transform, and outputs the digital signals Y₁-Y_(N) in parallel to the number N of the frequency up-conversion components 601, respectively. Each of the analog or digital signals Y₁-Y_(N) is a linear combination, i.e. weighted sum, each combined with the digital signals X₁-X_(N) multiplied by respective weightings, and distributions of the weightings of any two input components in all of the analog or digital signals Y₁-Y_(N) are orthogonal, which can be referred to as the description illustrated in FIGS. 1A and 1D. In this case, as illustrated in FIG. 1D, the number of H is equal to N. The wavefront multiplexer 213 has N*N computing units and four summing processors. The computing units form a processor array with four rows and four columns. The input signals X₁-X_(N) can be received by the computing units in the number N of respective columns in the processor array. Upon receiving the input signals X₁-X_(N), each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The number N of the summing processors can output the number N of the signals Y₁-Y_(N) each combined with the weighted signals output from the computing units in a corresponding one of the number N of the rows in the processor array. In a case, each of the digital signals X₁-X_(N) can be, but not limited to, an IF digital signal or a RF digital signal.

Next, referring to FIG. 6A, upon receiving the signals Y₁-Y_(N) output in parallel from the wave-front multiplexer 213, the number N of frequency up-conversion components 601 convert the number N of signals Y₁-Y_(N) into the number N of analog or digital microwave signals U₁-U_(N) each having or modulating a distinct carrier within a distinct frequency sub-band in a bandwidth, such as Ku frequency band or Ka frequency band, for satellite communication from any other one of the number N of signals U₁-U_(N), wherein the frequency sub-bands of the signals U₁-U_(N) are not overlapped to one another or each other.

Next, referring to FIG. 6A, upon receiving the signals U₁-U_(N), the output multiplexer (O-Mux) 602, i.e. a frequency division multiplexer (FDM), combines the number N of signals U₁-U_(N) into a signal analog or digital composite microwave signal P₀. Next, upon receiving the signal composite signal P₀, the antenna array 603 outputs or broadcasts an analog or digital microwave signal Q₀ carrying information associated with the signal P₀ to the satellite 650.

Next, referring to FIG. 6A, the satellite 650 is provided with a transponder, operating at multiple frequency sub-bands in a Ku or Ka frequency bandwidth, for example, that receives the microwave signal Q₀ from the uplink ground terminal 605, amplifies the microwave signal Q₀ and outputs an analog or digital microwave signal R₀ at a different frequency range from that of the microwave signal Q₀, wherein the microwave signal R₀ carries information associated with the microwave signal Q₀.

Next, referring to FIG. 6A, the antenna array 607 intercepts or receives the microwave signal R₀ from the satellite 650 and outputs the microwave signal K₀ carrying information associated with the microwave signal R₀. Next, upon receiving the microwave signal K₀ output from the antenna array 607, the input multiplexer 608, i.e. a frequency division demultiplexer (FDDM), divides the microwave signal K₀ into the number N of analog or digital microwave signals I₁-I_(N), wherein each of the microwave signals I₁-I_(N) has or modulates a distinct carrier within a distinct frequency sub-band in the Ku frequency band or Ka frequency band, for example, from any other one of the microwave signals I₁-I_(N), wherein the frequency sub-bands of the microwave signals I₁-I_(N) are not overlapped to one another or each other.

Next, referring to FIG. 6A, upon receiving the microwave signals I₁-I_(N) output in parallel from the input multiplexer 608, the frequency down-conversion components 609 convert the number N of microwave signals I₁-I_(N) into the number N of analog or digital signals W₁-W_(N) at an intermediate-frequency (IF) band or base band, for example, output to the equalizer 231 through multiple parallel channels, such as wireless channels or physical channels.

Next, referring to FIG. 6A, the above optimizing and equalizing process, as illustrated in FIG. 1C, is performed such that the digital signals W₁-W_(N) can be compensated to be multiplied by respective weightings by the equalizer 231, wherein the respective weightings of the equalizer 231 can be adjusted based on one or more control signals CS output from the optimizer 235. After the optimizing and equalizing process, the equalizer 231 outputs the number N of equalized analog or digital signals S₁-S_(N). For example, the equalized analog or digital signal S₁ is created by the equalizer 231 multiplying the analog or digital signal W₁ by a weighting of the equalizer 231. The equalized digital signal S_(N) is created by the equalizer 231 multiplying the digital signal W_(N) by another weighting of the equalizer 231. Each of the respective weightings of the equalizer 231 can be, but not limited to, a complex value such that the equalized signals S₁-S_(N) can be rotated precisely to become in phase. In this case, the equalizer 231 can be performed by the narrow band equalizer, as illustrated in FIG. 1C. The narrow band equalizer 231 can provide phase and amplitude modifications to each of the signals W₁-W_(N) featuring a constant phase shift and a constant amplitude attenuation across a narrow frequency band. Alternatively, the equalizer 231 can be performed by the broadband equalizer as illustrated in FIG. 1C. The broadband equalizer 231 can provide phase and amplitude modifications to each of the signals W₁-W₄ featuring a constant phase shift and a constant amplitude attenuation in each subband across a broad frequency band, but the phase shift and amplitude attenuation in one subband across the broad frequency band is different from those in the other sub-bands across the broad frequency band.

Next, referring to FIG. 6A, upon receiving, in parallel, the equalized digital signals S₁-S_(N) output in parallel from the equalizer 231, the wave-front demultiplexer 232 extracts multiple analog or digital signals Z₁-Z_(N), which are substantially equal to the analog or digital signals X₁-X_(N), respectively or to the digital signals X₁-X_(N) multiplied by the same scalar, respectively, from the analog or digital signals S₁-S_(N) by the above-mentioned wave-front demultiplexing transform, and outputs the analog or digital signals Z₁-Z_(N) in parallel, which can be referred to as the description illustrated in FIG. 1E. In this case, as illustrated in FIG. 1E, the number of I is equal to N. The wavefront demultiplexer 232 has N*N computing units and four summing processors. The computing units form a processor array with the number N of rows and the number N of columns. The input signals S₁-S_(N) can be received by the computing units in the number N of respective columns in the processor array. Upon receiving the input signals S₁-S_(N), each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The number N of the summing processors can output the number N of the signals Z₁-Z_(N) each combined with the weighted signals output from the computing units in a corresponding one of the number N of the rows in the processor array. Each of the signals Z₁-Z_(N) is a linear combination, i.e. weighted sum, each combined with the digital signals S₁-S_(N) multiplied by respective weightings, and distributions of the weightings of any two input components in all signals Z₁-Z_(N) are orthogonal, which can be referred to as the description illustrated in FIG. 1A.

Next, referring to FIG. 6A, upon receiving the signals Z₁-Z_(M), the M-to-1 time-domain multiplexer 610 combines or integrates the number M of signals Z₁-Z_(M) each having a bandwidth of J/M sampled as a sampling rate K/M into an analog or digital output signal B₀ having a bandwidth of J sampled as a sampling rate of K, wherein the output signal B₀ is substantially equal to the signal A₀ or to the signal A₀ multiplied by the same scalar as the digital signals X₁-X_(N) are multiplied. At the same time, the signals Z_(M+1)-Z_(N) are transmitted to the optimizer 231, the optimizer 235 generates the one or more control signals CS output to the equalizer 231 to adjust the respective weightings of the equalizers 231, as illustrated in FIG. 1C.

Besides, referring to FIG. 6B showing architecture as Satcom waveforms or signals spread through the number N of signal-channel-per-carrier (SCPC) channels with the same polarization in narrowband frequency slots over multiple satellites. The system 600 features point-to-point communications. The system 600 shown in FIG. 6B is similar to the system 600 illustrated in FIG. 6A except that the 1-to-M time-domain demultiplexer 604 illustrated in FIG. 6A is replaced with a 1-to-F time-domain demultiplexer 604 a for receiving an extraneous signal A₁ and a 1-to-G time-domain demultiplexer 604 b for receiving an extraneous signal A₂, as illustrated in FIG. 6B, that the output multiplexer 602 illustrated in FIG. 6A is replaced with two output multiplexers 602 a and 602 b for outputting two signals P₁ and P₂ to the antenna array 603, as illustrated in FIG. 6B, that the input multiplexer 602 illustrated in FIG. 6A is replaced with two input multiplexers 608 a and 608 b for receiving two signals K₁ and K₂ from the antenna array 607, as illustrated in FIG. 6B, that the M-to-1 time-domain demultiplexer 610 illustrated in FIG. 6A is replaced with a F-to-1 time-domain demultiplexer 610 a for outputting a signal B₁ and a G-to-1 time-domain demultiplexer 610 b for outputting a signal B₂, as illustrated in FIG. 6B, and that two satellites 650 a and 650 b are used to transmits signals from the antenna array 603 to the antenna 607.

Referring to FIG. 6B, a method for processing data streams is described as blow. The 1-to-F TDDM 604 a includes an input port receiving a digital or analog signal A₁ and the number F of output ports outputting the number F of digital or analog signals X₁-X_(F). The 1-to-F TDDM 604 a can divide the input signal A₁ having a frequency bandwidth of J1 sampled at a sampling rate of K1 into the number F of the signals X₁-X_(F), each having a frequency bandwidth of J1/F sampled at a sampling rate of K1/F, passing through the number F of parallel signal paths, such as physical or wireless channels, coupled to the wave-front multiplexer 213. The 1-to-G TDDM 604 b includes an input port receiving a digital or analog signal A₂ and the number G of output ports outputting the number G of digital or analog signals X_(F+1)-X_(M). The 1-to-G TDDM 604 b can divide the input signal A₂ having a frequency bandwidth of J2 sampled at a sampling rate of K2 into the number G of the output signals X_(F+1)-X_(M), each having a frequency bandwidth of J2/G sampled at a sampling rate of K2/G, passing through the number G of parallel signal paths, such as physical or wireless channels, coupled to the wave-front multiplexer 213.

Next, referring to FIG. 6B, the digital or analog signals X₁-X_(F) output from the 1-to-F time-domain demultiplexer (TDDM) 604 a, the digital or analog signals X_(F+1)-X_(M) output from the 1-to-G time-domain demultiplexer 604 a and one or more pilot or diagnostic signals X_(M+1)-X_(N) that can analog or digital ones are transmitted to the wavefront multiplexer 213. Each of the pilot or diagnostic signals X_(M+1)-X_(N) may be a pilot or diagnostic signal that may have a single frequency and fixed amplitude. Alternatively, the pilot or diagnostic signals X_(M+1)-X_(N) could change based on time or could be any signal known by the system 600. The extraneous signal A₁ divided into the number F of the digital or analog signals X₁-X_(F) by the 1-to-F time-domain demultiplexer 604 a and the extraneous signal A₂ divided into the number G of the digital or analog signals X_(F+1)-X_(M) by the 1-to-G time-domain demultiplexer 604 are unknown by the system 600 and input into the system 600 from one or more extraneous systems.

Next, referring to FIG. 6B, upon receiving, in parallel, the number M of the individual and independent digital signals X₁-X_(M) and the number N−M of pilot or diagnostic signals X_(M+1)-X_(N), the wave-front multiplexer 213 can processes the number N of the analog or digital signals X₁-X_(N) into the number N of analog or digital signals Y₁-Y_(N) by the above-mentioned wave-front multiplexing transform, and outputs the digital signals Y₁-Y_(N) in parallel to the number N of the frequency up-conversion components 601, respectively. More description and calculation related to the wave-front multiplexer 213 can be referred to as those illustrated in FIG. 6A.

Next, referring to FIG. 6B, upon receiving the signals Y₁-Y_(N) output in parallel from the wave-front multiplexer 213, the number N of frequency up-conversion components 601 convert the number N of signals Y₁-Y_(N) into the number N of analog or digital microwave signals U₁-U_(N) each having or modulating a distinct carrier within a distinct frequency sub-band in a bandwidth, such as Ku frequency band or Ka frequency band, for satellite communication from any other one of the number N of signals U₁-U_(N), wherein the frequency sub-bands of the signals U₁-U_(N) are not overlapped to one another or each other.

Next, referring to FIG. 6B, upon receiving the signals U₁-U_(S), the output multiplexer (O-Mux) 602 a, i.e. a frequency division multiplexer (FDM), combines the number S of signals U₁-U_(S) into a signal analog or digital composite microwave signal P₁. Upon receiving the signals U_(S+1)-U_(N), the output multiplexer (O-Mux) 602 b, i.e. a frequency division multiplexer (FDM), combines the number N−S of signals U_(S+1)-U_(N) into a signal analog or digital composite microwave signal P₂. Next, upon receiving the signal composite signals P₁ and P₂, the antenna array 603 outputs or broadcasts an analog or digital microwave signal Q₁ to the satellite 650 a and an analog or digital microwave signal Q₂ to the satellite 650 b, wherein the wave signal Q₁ could carry information associated with the signal P₁ but independent from the signal P₂ and the wave signal Q₂ could carry information associated with the signal P₂ but independent from the signal P₁. Alternatively, the wave signal Q₁ could carry information associated with the signals P₁ and P₂ and the wave signal Q₂ could carry information associated with the signal P₂ but independent from the signal P₁. Alternatively, the wave signal Q₁ could carry information associated with the signal P₁ but independent from the signal P₂ and the wave signal Q₂ could carry information associated with the signals P₁ and P₂. Alternatively, each of the wave signals Q₁ and Q₂ could carry information associated with the signal P₁ and P₂.

Next, referring to FIG. 6B, the satellite 650 a is provided with a transponder, operating at multiple frequency sub-bands in a Ku or Ka frequency bandwidth, for example, that receives the microwave signal Q₁ from the uplink ground terminal 605, amplifies the microwave signal Q₁ and outputs an analog or digital microwave signal R₁ at a different frequency range from that of the microwave signal Q₁ and that of the microwave signal Q₂, wherein the microwave signal R₁ carries information associated with the microwave signal Q₁. The satellite 650 b is provided with a transponder, operating at multiple frequency sub-bands in a Ku or Ka frequency bandwidth, for example, that receives the microwave signal Q₂ from the uplink ground terminal 605, amplifies the microwave signal Q₂ and outputs an analog or digital microwave signal R₂ at a different frequency range from that of the microwave signal Q₁ and that of the microwave signal Q₂, wherein the microwave signal R₂ carries information associated with the microwave signal Q₂.

Next, referring to FIG. 6B, the antenna array 607 intercepts or receives the microwave signal R₁ from the satellite 650 a and the microwave signal R₂ from the satellite 650 b and outputs the microwave signal K₁ to the input multiplexer 608 a and the microwave signal K₂ to the input multiplexer 608 b, wherein the wave signal K₁ could carry information associated with the signal R₁ but independent from the signal R₂ and the wave signal K₂ could carry information associated with the signal R₂ but independent from the signal R₁. Alternatively, the wave signal K₁ could carry information associated with the signals R₁ and R₂ and the wave signal K₂ could carry information associated with the signal R₂ but independent from the signal R₁. Alternatively, the wave signal K₁ could carry information associated with the signal R₁ but independent from the signal R₂ and the wave signal K₂ could carry information associated with the signals R₁ and R₂. Alternatively, each of the wave signals K₁ and K₂ could carry information associated with the signal R₁ and R₂.

Next, referring to FIG. 6B, upon receiving the microwave signal K₁ output from the antenna array 607, the input multiplexer 608 a, i.e. a frequency division demultiplexer (FDDM), divides the microwave signal K₁ into the number T of analog or digital microwave signals I₁-I_(T). Upon receiving the microwave signal K₂ output from the antenna array 607, the input multiplexer 608 b, i.e. a frequency division demultiplexer (FDDM), divides the microwave signal K₂ into the number N−T of analog or digital microwave signals I_(T+1)-I_(N). Each of the microwave signals I₁-I_(N) has or modulates a distinct carrier within a distinct frequency sub-band in the Ku frequency band or Ka frequency band, for example, from any other one of the microwave signals I₁-I_(N), wherein the frequency sub-bands of the microwave signals I₁-I_(N) are not overlapped to one another or each other.

Next, referring to FIG. 6B, upon receiving the microwave signals I₁-I_(N) output in parallel from the input multiplexers 608 a and 608 b, the frequency down-conversion components 609 convert the number N of microwave signals I₁-I_(N) into the number N of analog or digital signals W₁-W_(N) at an intermediate-frequency (IF) band or base band, for example, output to the equalizer 231 through multiple parallel channels, such as wireless channels or physical channels.

Next, referring to FIG. 6B, the above optimizing and equalizing process, as illustrated in FIG. 1C, is performed such that the digital signals W₁-W_(N) can be compensated to be multiplied by respective weightings by the equalizer 231, wherein the respective weightings of the equalizer 231 can be adjusted based on one or more control signals CS output from the optimizer 235. After the optimizing and equalizing process, the equalizer 231 outputs the number N of equalized analog or digital signals S₁-S_(N). More description and calculation related to the equalizer 231 can be referred to as those illustrated in FIG. 6A.

Next, referring to FIG. 6B, upon receiving, in parallel, the equalized digital signals S₁-S_(N) output in parallel from the equalizer 231, the wave-front demultiplexer 232 extracts multiple analog or digital signals Z₁-Z_(N), which are substantially equal to the analog or digital signals X₁-X_(N), respectively or to the digital signals X₁-X_(N) multiplied by the same scalar, respectively, from the analog or digital signals S₁-S_(N) by the above-mentioned wave-front demultiplexing transform. More description and calculation related to the wave-front demultiplexer 232 can be referred to as those illustrated in FIG. 6A.

Next, referring to FIG. 6B, upon receiving the signals Z₁-Z_(F), the F-to-1 time-domain multiplexer 610 a combines or integrates the number F of signals Z₁-Z_(F) each having a bandwidth of J1/F sampled as a sampling rate K1/F into an analog or digital output signal B₁ having a bandwidth of J1 sampled as a sampling rate of K1, wherein the output signal B₁ is substantially equal to the signal A₁ or to the signal A₁ multiplied by the same scalar as the digital signals X₁-X_(N) are multiplied. Upon receiving the signals Z_(F+1)-Z_(M), the G-to-1 time-domain multiplexer 610 b combines or integrates the number G of signals Z_(F+1)-Z_(M) each having a bandwidth of J2/G sampled as a sampling rate K2/G into an analog or digital output signal B₂ having a bandwidth of J2 sampled as a sampling rate of K2, wherein the output signal B₂ is substantially equal to the signal A₂ or to the signal A₂ multiplied by the same scalar as the digital signals X₁-X_(N) are multiplied. The signals B₁ and B₂ are substantially equal to the signals A₁ and A₂ respectively or to the signals B₁ and B₂ multiplied by the same scalar, respectively. At the same time, the signals Z_(M+1)-Z_(N) are transmitted to the optimizer 231, the optimizer 235 generates the one or more control signals CS output to the equalizer 231 to adjust the respective weightings of the equalizers 231, as illustrated in FIG. 1C.

In this case as above illustrated in FIG. 6B, the number of N is an integer that could be any number equal to or greater than 2, 4, 8, 16, 32, 64, 128 or 256. The number of M is an integer that could be any number less than the number of N. The number of F is an integer that could be any number less than the number of M. The number of G is an integer that could be any number less than the number of M and could be equal to or greater or less than the number of F. The number of S is an integer that could be any number less than the number of N and equal to or greater or less than an half of the number of N. The number of T is an integer that could be any number less than the number of N, equal to or greater or less than an half of the number of N and equal to or greater or less than the number of S. The number F plus the number G equals the number M.

Besides, FIG. 6C shows multipoint-to-point communications over multiple satellites. FIG. 6D shows architecture of uplink ground terminals 605 a and 605 b shown in FIG. 6C. Referring to FIGS. 6C and 6D, satcom waveforms or signals are shown to be spread through the number N of signal-channel-per-carrier (SCPC) channels with the same polarization in narrowband frequency slots over multiple satellites. The system 600 shown in FIGS. 6C and 6D is similar to that illustrated in FIG. 6B except that the system 600 illustrated in FIGS. 6C and 6D uses the number Nt of signal transmitting sources, such as including a first transmitting source 605 a, i.e. an uplink ground terminal, processing one, i.e. A₁, of the extraneous signals A₁ and A₂, and a second transmitting source 605 b, i.e. an uplink ground terminal, processing one, i.e. A₂, of the extraneous signals A₁ and A₂. The number Nr of signal receiving sources, such as including only one receiving source outputting the two signals B₁ and B₂ substantially equal to the signals A₁ and A₂ respectively or to the signals B₁ and B₂ multiplied by the same scalar, respectively. The number of Nt could be any number equal to or greater than 2, 3, 4, 5, 6, 7, 8, 9 or 10, and could be greater than the number of Nr that could be one in this embodiment. The number Nt of the transmitting sources have the same wavefront multiplexer as one another or each other and use different input ports in sequence for receiving different extraneous signals. For example, referring to FIG. 6C, the two transmitting sources 605 a and 605 b contains two wavefront multiplexers 213 a and 213 b each having the same architecture as each other, and the wavefront multiplexers 213 a and 213 b use different input ports in sequence for receiving the different signals X₁-X_(M), wherein the wavefront multiplexer 213 a has the number F of upper ports for receiving the signals X₁-X_(F) output from the 1-to-F time domain demultiplexer (TDDM) 604 a but the wavefront multiplexer 213 b has the number G of middle ports, for receiving the signals X_(F+1)-X_(M) output from the 1-to-G time domain demultiplexer 604 b, different in sequence from the upper ports of the wavefront multiplexer 213 a for receiving the signals X₁-X_(F). In this case, referring to FIG. 6C, the one or more pilot or diagnostic signals X_(M+1)-X_(N), input into the wavefront multiplexer 213 a, carry the same information in sequence as the pilot or diagnostic signals X_(M+1)-X_(N) input into the wavefront multiplexer 213 b. The other ports of the wavefront multiplexers 213 a and 213 b can be connected to a ground reference for receiving ground signals. The number Nt of the signal transmitting sources contains the number Nt of antenna arrays. In this case, the two signal transmitting sources 605 a and 605 b contains two antenna arrays 603 a and 603 b, respectively. Upon intercepting or receiving analog or digital microwave signals Q_(1a) and Q_(1b) output from the antenna arrays 603 a and 603 b, the satellite 650 a combines carriers at the same frequency sub-bands across the microwave signals Q_(1a) and Q_(1b) and outputs the microwave signal R₁ carrying information associated with the microwave signals Q_(1a) and Q_(1b) to the antenna array 607. Upon intercepting or receiving analog or digital microwave signals Q_(1a) and Q_(1b) output from the antenna arrays 603 a and 603 b, the satellite 650 a combines carriers at the same frequency sub-bands across the microwave signals Q_(2a) and Q_(2b) and outputs the microwave signal R₂ carrying information associated with the microwave signals Q_(2a) and Q_(2b) to the antenna array 607. There could be no synchronizations between the two transmitting sources 605 a and 605 b.

A method for processing signals or data streams by using the system 600 shown in FIGS. 6C and 6D is described below. The uplink ground terminal 605 a receives an extraneous analog or digital signal A₁ input to an input port of the 1-to-F TDDM 604 a. The 1-to-F TDDM 604 a includes the number F of output ports outputting the number F of digital or analog signals X₁-X_(F). The 1-to-F TDDM 604 a can divide the input signal A₁ having a frequency bandwidth of J1 sampled at a sampling rate of K1 into the number F of the signals X₁-X_(F), each having a frequency bandwidth of J1/F sampled at a sampling rate of K1/F, passing through the number F of parallel signal paths, such as physical or wireless channels, coupled to a wave-front multiplexer 213 a. The analog or digital signal X₁-X_(F) could be individual and independent from each other or one another. At the same time, the number G of ground signals and the number N-M of pilot or diagnostic signals are input in parallel to the wave-front multiplexer 213 a through multiple parallel signal paths, such as wireless channels or physical channels, wherein the number G of input ports of the wave-front multiplexer 213 a can be connected to a ground reference for receiving the ground signals. The ground signals represent no extraneous signals input to the input ports of the wave-front multiplexer 213 a. The digital pilot or diagnostic signals X_(M+1)-X_(N) may have a single frequency and fixed amplitude. Alternatively, the digital pilot or diagnostic signals X_(M+1)-X_(N) could change based on time or could be any signal known by the system 600. The extraneous analog or digital signal A₁ divided into the number F of the analog or digital signals X₁-X_(F) by the 1-to-F TDDM 604 a is unknown by the system 600 and input into the system 600 from an extraneous system.

Next, referring to FIGS. 6C and 6D, the wave-front multiplexer 213 a performs the above wave-front multiplexing transform to process the analog and digital signals X₁-X_(F), the number G of the ground signals and the pilot or diagnostic signals X_(M+1)-X_(N) into multiple linear combinations, each combined with the signals X₁-X_(F) and X_(M+1)-X_(N) and the ground signals multiplied by respective weightings, represented by the number N of digital signals Y_(1a)-Y_(Na), which can referred to as FIGS. 1A and 1D. In this case, as illustrated in FIG. 1D, the number of H is equal to N. The wavefront multiplexer 213 a has N*N computing units and the number N of summing processors. The computing units form a processor array with the number N of rows and the number N of columns. The signals X₁-X_(F) and X_(M+1)-X_(N) and the ground signals can be received by the computing units in the number N of the respective columns in the processor array. Upon receiving the input signals X₁-X_(F) and X_(M+1)-X_(N) and the ground signals, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The number N of the summing processors can output the signals Y_(1a)-Y_(Na) each combined with the weighted signals output from the computing units in a corresponding one of the number N of the rows in the processor array. The signals X₁-X_(F) and X_(M+1)-X_(N) can be, but not limited to, IF digital signals or RF digital signals.

Next, referring to FIGS. 6C and 6D, upon receiving the digital signals Y_(1a)-Y_(Na) output in parallel from the wave-front multiplexer 213 a, the number N of frequency up-conversion components 601 convert the number N of signals Y_(1a)-Y_(Na) into the number N of analog or digital microwave signals U_(1a)-U_(Na) each having or modulating a distinct carrier within a distinct frequency sub-band in a bandwidth, such as Ku frequency band or Ka frequency band, for satellite communication from any other one of the number N of signals U_(1a)-U_(Na), wherein the frequency sub-bands of the signals U_(1a)-U_(Na) are not overlapped to one another or each other.

Next, referring to FIGS. 6C and 6D, upon receiving the signals U_(1a)-U_(Sa), the output multiplexer (O-Mux) 602 a, i.e. a frequency division multiplexer (FDM), combines the number S of signals U_(1a)-U_(Sa) into a signal analog or digital composite microwave signal P_(1a). Upon receiving the signals U_(Sa+1)-U_(Na), the output multiplexer (O-Mux) 602 b, i.e. a frequency division multiplexer (FDM), combines the number N−S of signals U_(Sa+1)-U_(Na) into a signal analog or digital composite microwave signal P_(2a). Next, upon receiving the signal composite signals P_(1a) and P_(2a), the antenna array 603 a outputs or broadcasts an analog or digital microwave signal Q_(1a) to the satellite 650 a and an analog or digital microwave signal Q_(2a) to the satellite 650 b, wherein the wave signal Q_(1a) could carry information associated with the signal P_(1a) but independent from the signal P_(2a) and the wave signal Q_(2a) could carry information associated with the signal P_(2a) but independent from the signal P_(1a). Alternatively, the wave signal Q_(1a) could carry information associated with the signals P_(1a) and P_(2a) and the wave signal Q_(2a) could carry information associated with the signal P_(2a) but independent from the signal P_(1a). Alternatively, the wave signal Q_(1a) could carry information associated with the signal P_(1a) but independent from the signal P_(2a) and the wave signal Q_(2a) could carry information associated with the signals P_(1a) and P_(2a). Alternatively, each of the wave signals Q_(1a) and Q_(2a) could carry information associated with the signal P_(1a) and P_(2a).

Referring to FIGS. 6C and 6D, with regards to the uplink ground terminal 605 b receiving an extraneous analog or digital signal A₂, the extraneous analog or digital signal A₂ is input to an input port of the 1-to-G TDDM 604 b. The 1-to-G TDDM 604 b includes the number G of output ports outputting the number G of digital or analog signals X_(F+1)-X_(M). The 1-to-G TDDM 604 b can divide the input signal A₂ having a frequency bandwidth of J2 sampled at a sampling rate of K2 into the number G of the signals X_(F+1)-X_(M), each having a frequency bandwidth of J2/G sampled at a sampling rate of K2/G, passing through the number G of parallel signal paths, such as physical or wireless channels, coupled to a wave-front multiplexer 213 b. The analog or digital signal X_(F+1)-X_(M) could be individual and independent from each other or one another. At the same time, the number F of ground signals and the number N−M of pilot or diagnostic signals are input in parallel to the wave-front multiplexer 213 b through multiple parallel signal paths, such as wireless channels or physical channels, wherein the number F of input ports of the wave-front multiplexer 213 a can be connected to a ground reference for receiving the ground signals. The ground signals represent no extraneous signals input to the input ports of the wave-front multiplexer 213 b. The digital pilot or diagnostic signals X_(M+1)-X_(N) may have a single frequency and fixed amplitude. Alternatively, the digital pilot or diagnostic signals X_(M+1)-X_(N) could change based on time or could be any signal known by the system 600. The extraneous analog or digital signal A₂ divided into the number G of the analog or digital signals X_(F+1)-X_(M) by the 1-to-G TDDM 604 b is unknown by the system 600 and input into the system 600 from an extraneous system.

Next, referring to FIGS. 6C and 6D, the wave-front multiplexer 213 b performs the above wave-front multiplexing transform to process the analog and digital signals X_(F+1)-X_(M), the number F of the ground signals and the pilot or diagnostic signals X_(M+1)-X_(N) into multiple linear combinations, each combined with the signals X_(F+1)-X_(M) and X_(M+1)-X_(N) and the ground signals multiplied by respective weightings, represented by the number N of digital signals Y_(1b)-Y_(Nb), which can referred to as FIGS. 1A and 1D. In this case, as illustrated in FIG. 1D, the number of H is equal to N. The wavefront multiplexer 213 a has N*N computing units and the number N of summing processors. The computing units form a processor array with the number N of rows and the number N of columns. The signals X_(F+1)-X_(M) and X_(M+1)-X_(N) and the ground signals can be received by the computing units in the number N of the respective columns in the processor array. Upon receiving the input signals X_(F+1)-X_(M) and X_(M+1)-X_(N) and the ground signals, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The number N of the summing processors can output the signals Y_(1b)-Y_(M), each combined with the weighted signals output from the computing units in a corresponding one of the number N of the rows in the processor array. The signals X_(F+1)-X_(M) and X_(M+1)-X_(N) can be, but not limited to, IF digital signals or RF digital signals.

Next, referring to FIGS. 6C and 6D, upon receiving the digital signals Y_(1b)-Y_(Nb) output in parallel from the wave-front multiplexer 213 b, the number N of frequency up-conversion components 601 convert the number N of signals Y_(1b)-Y_(Nb) into the number N of analog or digital microwave signals U_(1b)-U_(Nb) each having or modulating a distinct carrier within a distinct frequency sub-band in a bandwidth, such as Ku frequency band or Ka frequency band, for satellite communication from any other one of the number N of signals U_(1b)-U_(Nb), wherein the frequency sub-bands of the signals U_(1b)-U_(Nb) are not overlapped to one another or each other.

Next, referring to FIGS. 6C and 6D, upon receiving the signals U_(1b)-U_(Lb), the output multiplexer (O-Mux) 602 c, i.e. a frequency division multiplexer (FDM), combines the number L of signals U_(1b)-U_(Lb) into a signal analog or digital composite microwave signal P_(1b). Upon receiving the signals U_(Lb+1)-U_(Nb), the output multiplexer (O-Mux) 602 b, i.e. a frequency division multiplexer (FDM), combines the number N-L of signals U_(Lb+1)-U_(Nb) into a signal analog or digital composite microwave signal P_(2b). Next, upon receiving the signal composite signals P_(1b) and P_(2b), the antenna array 603 b outputs or broadcasts an analog or digital microwave signal Q_(1b) to the satellite 650 a and an analog or digital microwave signal Q_(2b) to the satellite 650 b, wherein the wave signal Q_(1b) could carry information associated with the signal P_(1b) but independent from the signal P_(2b) and the wave signal Q_(2b) could carry information associated with the signal P_(2b) but independent from the signal P_(1b). Alternatively, the wave signal Q_(1b) could carry information associated with the signals P_(1b) and P_(2b) and the wave signal Q_(2b) could carry information associated with the signal P_(2b) but independent from the signal P_(1b). Alternatively, the wave signal Q_(1b) could carry information associated with the signal P_(1b) but independent from the signal P_(2b) and the wave signal Q_(2b) could carry information associated with the signals P_(1b) and P_(2b). Alternatively, each of the wave signals Q_(1b) and Q_(2b) could carry information associated with the signal P_(1b) and P_(2b).

Next, referring to FIGS. 6C and 6D, the satellite 650 a is provided with a transponder, operating at multiple frequency sub-bands in a Ku or Ka frequency bandwidth, for example, that receives the microwave signal Q_(1a) from the uplink ground terminal 605 a and the microwave signal Q_(1b) from the uplink ground terminal 605 b, amplifies the microwave signals Q_(1a) and Q_(1b) and outputs an analog or digital microwave signal R₁ at different frequency ranges from those of the microwave signal Q_(1a), Q_(1b), Q_(2a) and Q_(2b) respectively, wherein the microwave signal R₁ carries information associated with the microwave signals Q_(1a) and Q_(1b) and the microwave signal R₂ carries information associated with the microwave signal Q_(2a) and Q_(2b). The satellite 650 b is provided with a transponder, operating at multiple frequency sub-bands in a Ku or Ka frequency bandwidth, for example, that receives the microwave signal Q_(2a) and Q_(2b) from the uplink ground terminal 605 b, amplifies the microwave signals Q_(2a) and Q_(2b) and outputs an analog or digital microwave signal R₂ at a different frequency range from those of the microwave signal Q_(1a), Q_(1b), Q_(2a) and Q_(2b) respectively, wherein the microwave signal R₂ carries information associated with the microwave signal Q_(2a) and Q_(2b).

Next, referring to FIGS. 6C and 6D, the antenna array 607 intercepts or receives the microwave signal R₁ from the satellite 650 a and the microwave signal R₂ from the satellite 650 b and outputs the microwave signal K₁ to the input multiplexer 608 a and the microwave signal K₂ to the input multiplexer 608 b, wherein the wave signal K₁ could carry information associated with the signal R₁ but independent from the signal R₂ and the wave signal K₂ could carry information associated with the signal R₂ but independent from the signal R₁. Alternatively, the wave signal K₁ could carry information associated with the signals R₁ and R₂ and the wave signal K₂ could carry information associated with the signal R₂ but independent from the signal R₁. Alternatively, the wave signal K₁ could carry information associated with the signal R₁ but independent from the signal R₂ and the wave signal K₂ could carry information associated with the signals R₁ and R₂. Alternatively, each of the wave signals K₁ and K₂ could carry information associated with the signal R₁ and R₂.

Next, referring to FIGS. 6C and 6D, upon receiving the microwave signal K₁ output from the antenna array 607, the input multiplexer 608 a, i.e. a frequency division demultiplexer (FDDM), divides the microwave signal K₁ into the number T of analog or digital microwave signals I₁-I_(T). Upon receiving the microwave signal K₂ output from the antenna array 607, the input multiplexer 608 b, i.e. a frequency division demultiplexer (FDDM), divides the microwave signal K₂ into the number N−T of analog or digital microwave signals I_(T+1)-I_(N). Each of the microwave signals I₁-I_(N) has or modulates a distinct carrier within a distinct frequency sub-band in the Ku frequency band or Ka frequency band, for example, from any other one of the microwave signals I₁-I_(N), wherein the frequency sub-bands of the microwave signals I₁-I_(N) are not overlapped to one another or each other.

Next, referring to FIGS. 6C and 6D, upon receiving the microwave signals I₁-I_(N) output in parallel from the input multiplexers 608 a and 608 b, the frequency down-conversion components 609 convert the number N of microwave signals I₁-I_(N) into the number N of analog or digital signals W₁-W_(N) at an intermediate-frequency (IF) band or base band, for example, output to the equalizer 231 through multiple parallel channels, such as wireless channels or physical channels.

Next, referring to FIGS. 6C and 6D, the above optimizing and equalizing process, as illustrated in FIG. 1C, is performed such that the digital signals W₁-W_(N) can be compensated to be multiplied by respective weightings by the equalizer 231, wherein the respective weightings of the equalizer 231 can be adjusted based on one or more control signals CS output from the optimizer 235. After the optimizing and equalizing process, the equalizer 231 outputs the number N of equalized analog or digital signals S₁-S_(N). More description and calculation related to the equalizer 231 can be referred to as those illustrated in FIG. 6A.

Next, referring to FIGS. 6C and 6D, upon receiving, in parallel, the equalized digital signals S₁-S_(N) output in parallel from the equalizer 231, the wave-front demultiplexer 232 extracts multiple analog or digital signals Z₁-Z_(N), which are substantially equal to the analog or digital signals X₁-X_(N), respectively or to the digital signals X₁-X_(N) multiplied by the same scalar, respectively, from the analog or digital signals S₁-S_(N) by the above-mentioned wave-front demultiplexing transform. More description and calculation related to the wave-front demultiplexer 232 can be referred to as those illustrated in FIG. 6A.

Next, referring to FIGS. 6C and 6D, upon receiving the signals Z₁-Z_(F), the F-to-1 time-domain multiplexer 610 a combines or integrates the number F of signals Z₁-Z_(F) each having a bandwidth of J1/F sampled as a sampling rate K1/F into an analog or digital output signal B₁ having a bandwidth of J1 sampled as a sampling rate of K1, wherein the output signal B₁ is substantially equal to the signal A₁ or to the signal A₁ multiplied by the same scalar as the digital signals X₁-X_(N) are multiplied. Upon receiving the signals Z_(F+1)-Z_(M), the G-to-1 time-domain multiplexer 610 b combines or integrates the number G of signals Z_(F+1)-Z_(M) each having a bandwidth of J2/G sampled as a sampling rate K2/G into an analog or digital output signal B₂ having a bandwidth of J2 sampled as a sampling rate of K2, wherein the output signal B₂ is substantially equal to the signal A₂ or to the signal A₂ multiplied by the same scalar as the digital signals X₁-X_(N) are multiplied. The signals B₁ and B₂ are substantially equal to the signals A₁ and A₂ respectively or to the signals B₁ and B₂ multiplied by the same scalar, respectively. At the same time, the signals Z_(M+1)-Z_(N) are transmitted to the optimizer 231, the optimizer 235 generates the one or more control signals CS output to the equalizer 231 to adjust the respective weightings of the equalizer 231, as illustrated in FIG. 1C.

In this case as above illustrated in FIGS. 6C and 6D, the number of N is an integer that could be any number equal to or greater than 2, 4, 8, 16, 32, 64, 128 or 256. The number of M is an integer that could be any number less than the number of N. The number of F is an integer that could be any number less than the number of M. The number of G is an integer that could be any number less than the number of M and could be equal to or greater or less than the number of F. The number of S is an integer that could be any number less than the number of N and equal to or greater or less than an half of the number of N. The number of T is an integer that could be any number less than the number of N, equal to or greater or less than an half of the number of N and equal to or greater or less than the number of S. The number of L is an integer that could be any number less than the number of N, equal to or greater or less than an half of the number of N, equal to or greater or less than the number of S and equal to or greater or less than the number of T. The number F plus the number G equals the number M.

Sixth Embodiment: Application to Power Amplifier

FIG. 7A depicts a system of sharing output power to multiple input signals using a wave-front multiplexer, multiple power amplifiers and a wave-front demultiplexer according to an exemplary embodiment of the present disclosure.

Referring to FIG. 7A, a power amplifying system 300 may include a wave-front multiplexer 213, four power amplifiers (PAs) 320 a-320 d, and a wave-front demultiplexer 232. In this embodiment, the four processing units or devices 999 a-999 d as illustrated in FIG. 1A can be replaced with the four power amplifiers 320 a-320 d illustrated in FIG. 2A.

Referring to FIG. 7A, the wave-front multiplexer 213 after receiving, in parallel, four individual and independent analog or digital signals X₁-X₄, processes all the analog or digital signals X₁-X₄ into four analog or digital signals Y₁-Y₄ by the above-mentioned wave-front multiplexing transform, and outputs the analog or digital signals Y₁-Y₄ in parallel, which can be referred to as the description illustrated in FIG. 1A. Each of the analog or digital signals Y₁-Y₄ is a linear combination, i.e. weighted sum, of all the analog or digital signals X₁-X₄ multiplied by respective weightings, and distributions of the weightings of any two input components in all analog or digital signals Y₁-Y₄ are orthogonal, which can be referred to as the description illustrated in FIGS. 1A and 1D. In this case, as illustrated in FIG. 1D, the number of H is equal to 4. The wave-front multiplexer 213 may include 4*4 computing units and four summing processors. The computing units form a processor array with four rows and four columns. The input signals X₁-X₄ can be received by the computing units in the respective four columns in the processor array. Upon receiving the input signals X₁-X₄, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The four summing processors can output the four signals Y₁-Y₄ each combined with the weighted signals output from the computing units in a corresponding one of the four rows in the processor array. Each of the analog or digital signals X₁-X₄ can be, but not limited to, an IF digital signal or a RF digital signal.

Referring to FIG. 7A, the wave-front demultiplexer 232 can receive, in parallel, multiple coherently-combined digital signals S₁, S₂, S₃ and S₄ output in parallel from the power amplifiers 320 a-320 d, extracts multiple coherently combined analog or digital signals Z₁-Z₄, which are the analog or digital signals X₁-X₄ powered by substantially the same gain respectively or the analog or digital signals X₁-X₄ powered by different gains respectively, from the analog or digital signals S₁-S₄ by the above-mentioned wave-front demultiplexing transform, and outputs the analog or digital signals Z₁-Z₄ in parallel, which can be referred to as the description illustrated in FIG. 1A. Each of the analog or digital signals Z₁-Z₄ is a linear combination, i.e. weighted sum, of all the analog or digital signals S₁-S₄ multiplied by respective weightings, and distributions of the weightings of any two input components in all analog or digital signals Z₁-Z₄ are orthogonal, which can be referred to as the description illustrated in FIGS. 1A and 1E. In this case, the number of I is equal to 4. The wave-front demultiplexer 232 may include 4*4 computing units and four summing processors. The computing units form a processor array with four rows and four columns. The input signals S₁-S₄ can be received by the computing units in the respective four columns in the processor array. Upon receiving the input signals S₁-S₄, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The four summing processors can output the four signals Z₁-Z₄ each combined with the weighted signals output from the computing units in a corresponding one of the four rows in the processor array. Each of the analog or digital signals Z₁-Z₄ can be, but not limited to, an IF digital signal or a RF digital signal.

Referring to FIG. 7A, the four power amplifiers 320 a-320 d operating in near linear modes, that is the output power level of a power amplifier is proportional to the input power level of the power amplifier, are arranged in four parallel signal paths between the wave-front multiplexer 213 and the wave-front demultiplexer 232 of the system 300. In other words, the power amplifier 320 a is arranged in a first signal path between an output port 3 a of the wave-front multiplexer 213 and an input port 6 a of the wave-front demultiplexer 232 of the system 300. The power amplifier 320 b is arranged in a second signal path between an output port 3 b of the wave-front multiplexer 213 and an input port 6 b of the wave-front demultiplexer 232 of the system 300. The power amplifier 320 c is arranged in a third signal path between an output port 3 c of the wave-front multiplexer 213 and an input port 6 c of the wave-front demultiplexer 232 of the system 300. The analog-to-digital converter 220 d is arranged in a fourth signal path between an output port 3 d of the wave-front multiplexer 213 and an input port 6 d of the wave-front demultiplexer 232 of the system 300.

Referring to FIG. 7A, each of the power amplifiers 320 a-220 d can power a corresponding one of the four signals Y₁-Y₄ by a specific gain. For instance, each of the power amplifiers 320 a-220 d has a corresponding input port 4 a, 4 b, 4 c or 4 d for receiving a corresponding one of the analog or digital signals Y₁-Y₄ and a corresponding output port 5 a, 5 b, 5 c or 5 d for outputting a corresponding one of the analog or digital signal S₁-S₄. The analog or digital signals S₁-S₄ passing in parallel can be transmitted to parallel input ports 6 a-6 d of the wave-front demultiplexer 232 through parallel channels, such as wireless channels or physical channels, respectively.

A method for processing signals or data streams by using the system 300 is described below. Referring to FIG. 7A, the individual and independent analog or digital signals X₁-X₄ from, e.g., one or more wireless base stations or array elements such as antenna array elements are input in parallel to the input ports 2 a-2 d of the wave-front multiplexer 213 through, e.g., four parallel signal paths, four parallel wireless channels or four parallel physical channels. Each of the wireless base stations can be, but not limited to, a mobile base station or a Wi-Fi base station. Alternatively, the analog signals X₁-X₄ can come from, but not limited to, one or more microphone devices, one or more image sensors, one or more micro-electro-mechanical-system (MEMS) microphone chips, or one or more antennas of a mobile phone. After the analog or digital signals X₁-X₄ are input in parallel to the wave-front multiplexer 213, the wave-front multiplexer 213 performs the above-mentioned wave-front multiplexing transformation to process the individual analog or digital signals X₁-X₄ into multiple linear combinations, each combined with the analog or digital signals X₁-X₄ multiplied by respective weightings, represented by the analog or digital signals Y₁-Y₄. Next, the wave-front multiplexer 213 outputs the four analog or digital signals Y₁-Y₄ from its four output ports 3 a-3 d, and the four analog or digital signals Y₁-Y₄ are transmitted to the four input ports 4 a-4 d of the four power amplifiers 320 a-320 d, respectively, through four parallel channels, such as wireless channels or physical channels.

Referring to FIG. 7A, After the analog or digital signals Y₁-Y₄ are transmitted in parallel into the power amplifiers 320 a-320 d arranged in parallel, the power amplifiers 320 a-320 d power the analog or digital signals Y₁-Y₄ by the same gain or different gains respectively and output the four analog or digital signals S₁-S₄ in parallel from the four output ports 5 a-5 d of the power amplifiers 320 a-320 d. For example, the analog or digital signal S₁ features the analog or digital signal Y₁ powered by a first gain of the power amplifier 320 a. The analog or digital signal S₂ features the analog or digital signal Y₂ powered by a second gain of the power amplifier 320 b. The analog or digital signal S₃ features the analog or digital signal Y₃ powered by a third gain of the power amplifier 320 c. The analog or digital signal S₄ features the analog or digital signal Y₄ powered by a fourth gain of the power amplifier 320 d. In a case, the first, second, third and fourth gains can be substantially equal to one another. Alternatively, some of the first, second, third and fourth gains, such as first, second and third gains, can be substantially equal to each other or one another, and two of the first, second, third and fourth gains, such as first and fourth gains, can be different from each other. Alternatively, the first, second, third and fourth gains can be different from one another. The power amplifiers 320 a-320 d, for example, could be realized by four integrated circuit chips embedded in a single chip package, by four integrated circuit chips embedded in four individual chip packages, or by a single integrated circuit chip. Alternatively, the function of the power amplifiers 320 a-320 d can be realized by software installed in the system 300.

Next, referring to FIG. 7A, the analog or digital signals S₁-S₄ are transmitted in parallel into the four input ports 6 a-6 d of the wave-front demultiplexer 232 through four parallel channels, such as wireless channels or physical channels. The input ports 6 a-6 d are arranged in parallel. Next, the wave-front demultiplexer 232 performs the above-mentioned wave-front demultiplexing transformation to process the analog or digital signals S₁-S₄ into multiple linear combinations, each combined with the analog or digital signals S₁-S₄ multiplied by respective weightings, represented by the analog or digital signals Z₁-Z₄ output in parallel from the four parallel output ports 7 a-7 d of the wave-front demultiplexer 232. The four output ports 7 a-7 d are arranged in parallel. The analog or digital signals Z₁-Z₄ are the analog or digital signals X₁-X₄ powered by substantially the same gain respectively or the analog or digital signals X₁-X₄ powered by different gains respectively. For example, the analog or digital signal Z₁ features the analog or digital signal X₁ powered by a fifth gain of the system 300. The analog or digital signal Z₂ features the analog or digital signal X₂ powered by a sixth gain of the system 300. The analog or digital signal Z₃ features the analog or digital signal X₃ powered by a seventh gain of the system 300. The analog or digital signal Z₄ features the analog or digital signal X₄ powered by an eighth gain of the system 300. In a case, the fifth, sixth, seventh and eighth gains can be substantially equal to one another. Alternatively, some of the fifth, sixth, seventh and eighth gains, such as fifth, sixth and seventh gains, can be substantially equal to each other or one another, and two of the fifth, sixth, seventh and eighth gains, such as fifth and eighth gains, can be different from each other. Alternatively, the fifth, sixth, seventh and eighth gains can be different from one another. The power amplifiers 320 a-320 d, for example, could be realized by four integrated circuit chips embedded in a single chip package, by four integrated circuit chips embedded in four individual chip packages, or by a single integrated circuit chip.

According to another exemplary embodiment of the present disclosure, as seen in FIG. 7B, the system 300 may further include an equalizer to adjust the analog or digital signals Y₁-Y₄ output from the wave-front multiplexer 231 before the digital signals Y₁-Y₄ are transmitted into the power amplifiers 320 a-320 d. The system 300 illustrated in FIG. 7B is similar to that illustrated in FIG. 7A except that the system 300 illustrated in FIG. 7B further includes the equalizer 231. In FIG. 7B, the wave-front multiplexer 213 and the equalizer 231 can be, but not limited to, embedded in a module, processor, integrated-circuit chip, system-on chip or chip package 310.

A method for processing signals or data streams by using the system 300 shown in FIG. 7B is described below. The four extraneous analog or digital signals X₁-X₄ can be input from one or more wireless base stations or antenna array elements to the input ports 2 a-2 d of the wave-front multiplexer 213 through four parallel signal paths, four parallel wireless channels or four parallel physical channels. Each of the wireless base stations can be, but not limited to, a mobile base station or a Wi-Fi base station. Alternatively, the analog or digital signals X₁-X₄ can come from, but not limited to, one or more microphone devices, one or more image sensors, one or more MEMS microphone chips, or one or more antennas of a mobile phone. The extraneous analog or digital signals X₁-X₄ could be independent from one another.

Next, referring to FIG. 7B, the wave-front multiplexer 213 performs the above wave-front multiplexing transformation to process the signals X₁-X₄ into multiple linear combinations, each combined with the signals X₁-X₄ multiplied by respective weightings, represented by four analog or digital signals Y₁-Y₄. Next, the wave-front multiplexer 213 outputs the analog or digital signals Y₁-Y₄ from its output ports 3 a-3 d, and the analog or digital signals Y₁-Y₄ are respectively transmitted to four input ports 10 a-10 d of the equalizer 231 through four parallel channels, such as wireless channels or physical channels.

Referring to FIG. 7B, upon receiving the analog or digital signals Y₁-Y₄, the equalizer 231 performs an equalizing process to the analog or digital signals Y₁-Y₄ such that the digital signals Y₁-Y₄ can be compensated to be multiplied by four respective weightings, and then outputs four equalized digital signals W₁-W₄, respectively, from its output ports 11 a-11 d. The equalized digital signal W₁ is created by the equalizer 231 multiplying the analog or digital signal Y₁ by a weighting of the equalizer 231. The equalized digital signal W₂ is created by the equalizer 231 multiplying the analog or digital signal Y₂ by another weighting of the equalizer 231. The equalized digital signal W₃ is created by the equalizer 231 multiplying the analog or digital signal Y₃ by another weighting of the equalizer 231. The equalized digital signal W₄ is created by the equalizer 231 multiplying the analog or digital signal Y₄ by the other weighting of the equalizer 231. Each of the four respective weightings of the equalizer 231 can be, but not limited to, a complex value such that the equalized signals W₁-W₄ can be rotated precisely to become in phase. In this case, the equalizer 231 can be performed by the narrow band equalizer, as illustrated in FIG. 1C. The narrow band equalizer 231 can provide phase and amplitude modifications to each of the signals Y₁-Y₄ featuring a constant phase shift and a constant amplitude attenuation across the narrow frequency band. Alternatively, the equalizer 231 can be performed by the broadband equalizer, as illustrated in FIG. 1C. The broadband equalizer 231 can provide phase and amplitude modifications to each of the signals Y₁-Y₄ featuring a constant phase shift and a constant amplitude attenuation in each sub-band across the broad frequency band, but the phase shift and amplitude attenuation in one sub-band across the broad frequency band is different from those in the other sub-band across the broad frequency band.

Next, referring to FIG. 7B, the equalized digital signals W₁-W₄ are transmitted in parallel to the input ports 4 a-4 d of the power amplifiers 320 a-320 d operating in near linear modes. Upon receiving the equalized digital signals W₁-W₄, the power amplifiers 320 a-320 d power the analog or digital signals W₁-W₄ by the same gain or different gains respectively and output four analog or digital signals S₁-S₄ in parallel from the four output ports 5 a-5 d of the power amplifiers 320 a-320 d. For example, the analog or digital signal S₁ features the analog or digital signal W₁ powered by the first gain of the power amplifier 320 a. The analog or digital signal S₂ features the analog or digital signal W₂ powered by the second gain of the power amplifier 320 b. The analog or digital signal S₃ features the analog or digital signal W₃ powered by the third gain of the power amplifier 320 c. The analog or digital signal S₄ features the analog or digital signal W₄ powered by the fourth gain of the power amplifier 320 d. In a case, the first, second, third and fourth gains can be substantially equal to one another. Alternatively, some of the first, second, third and fourth gains, such as first, second and third gains, can be substantially equal to each other or one another, and two of the first, second, third and fourth gains, such as first and fourth gains, can be different from each other. Alternatively, the first, second, third and fourth gains can be different from one another. The power amplifiers 320 a-320 d, for example, could be realized by four integrated circuit chips embedded in a single chip package, by four integrated circuit chips embedded in four individual chip packages, or by a single integrated circuit chip. Alternatively, the function of the power amplifiers 320 a-320 d can be realized by software installed in the system 300.

Next, referring to FIG. 7B, the analog or digital signals S₁-S₄ are transmitted in parallel into the four input ports 6 a-6 d of the wave-front demultiplexer 232 through four parallel channels, such as wireless channels or physical channels. The input ports 6 a-6 d are arranged in parallel. Upon on receiving the analog or digital signals S₁-S₄, the wave-front demultiplexer 232 performs the above-mentioned wave-front demultiplexing transformation to process the analog or digital signals S₁-S₄ into multiple linear combinations, each combined with the analog or digital signals S₁-S₄ multiplied by respective weightings, represented by the analog or digital signals Z₁-Z₄ output in parallel from the four parallel output ports 7 a-7 d of the wave-front demultiplexer 232. The four output ports 7 a-7 d are arranged in parallel. The analog or digital signals Z₁-Z₄ are the analog or digital signals X₁-X₄ powered by substantially the same gain respectively or the analog or digital signals X₁-X₄ powered by different gains respectively. For example, the analog or digital signal Z₁ features the analog or digital signal X₁ powered by a fifth gain of the system 300. The analog or digital signal Z₂ features the analog or digital signal X₂ powered by a sixth gain of the system 300. The analog or digital signal Z₃ features the analog or digital signal X₃ powered by a seventh gain of the system 300. The analog or digital signal Z₄ features the analog or digital signal X₄ powered by an eighth gain of the system 300. In a case, the fifth, sixth, seventh and eighth gains can be substantially equal to one another. Alternatively, some of the fifth, sixth, seventh and eighth gains, such as fifth, sixth and seventh gains, can be substantially equal to each other or one another, and two of the fifth, sixth, seventh and eighth gains, such as fifth and eighth gains, can be different from each other. Alternatively, the fifth, sixth, seventh and eighth gains can be different from one another. The power amplifiers 320 a-320 d, for example, could be realized by four integrated circuit chips embedded in a single chip package, by four integrated circuit chips embedded in four individual chip packages, or by a single integrated circuit chip.

According to another exemplary embodiment of the present disclosure, as seen in FIG. 7C, the system 300 may further include an optimizer 235 to adjust the weightings of the equalizer 231. The system 300 illustrated in FIG. 7C is similar to that illustrated in FIG. 7B except that the system 300 illustrated in FIG. 7C further includes the optimizer 235 and the analog or digital signal X₄ is input as a pilot or diagnostic signal. The pilot or diagnostic signal X₄ may have a single frequency and fixed amplitude. Alternatively, the analog pilot or diagnostic signal X₄ could change based on time or could be any signal known by the system 300. The extraneous analog or digital signals X₁-X₃ are unknown by the system 300 and input into the system 300 from an extraneous system, wherein the analog or digital signals X₁-X₃ are at least 20 dB above that of the pilot or diagnostic signal X₄. It will only consume 1% or less output power. The optimizer 235 can be in a signal path between the output ports 7 a-7 d of the wave-front demultiplexer 232 and the equalizer 231 (only one signal path between the output port 7 d and the equalizer 231 is shown in FIG. 7C). In FIG. 7C, the wave-front multiplexer 213 and the equalizer 231 can be, but not limited to, integrated or embedded in a module, processor, integrated-circuit chip, system-on chip or chip package 310, and the optimizer 235 can be, but not limited to, embedded in another module, processor, integrated-circuit chip, system-on chip or chip package. Alternatively, the wave-front multiplexer 213, the equalizer 231 and the optimizer 235 can be, but not limited to, integrated or embedded in the module, processor, integrated-circuit chip, system-on chip or chip package 310.

Following the above steps illustrated in FIG. 7B, after the signals Z₁-Z₄ are output from the wave-front demultiplexer 232, upon receiving the signal Z₄, the optimizer 235 shown in FIG. 7C is configured to calculate a difference between a value represented by the diagnostic signal Z₄ and a predetermined value known by the system 300, wherein the diagnostic signal X₄, input into the wave-front multiplexer 213, corresponding to the diagnostic signal Z₄ represents the predetermined value. Alternatively, upon receiving the signals Z₁-Z₄, the optimizer 235 may be configured further to calculate correlations between the signals Z₁ and Z₂, between the signals Z₁ and Z₃, between the signals Z₁ and Z₄, between the signals Z₂ and Z₃, between the signals Z₂ and Z₄, and the signals Z₃ and Z₄. Next, the optimizer 235 is configured to calculate a sum value, i.e. cost, by performing weighted summation of multiple factors including the difference. Alternatively, the factors may further include the correlations in case that the correlations are obtained. Next, the optimizer 235 is configured to compare the calculated sum value or cost with a threshold sum value, i.e. threshold cost. Next, the optimizer 235 is configured to calculate a variation in the calculated sum value or cost in response to finding the calculated sum value or cost is greater than the threshold sum value or threshold cost. The optimizer 235 creates a control signal CS based on the variation and transmits the control signal CS to the equalizer 231 so as to adjust the four weightings of the equalizer 231. The optimizer 235 is configured to stop the above loop in response to finding the calculated sum value or cost is less than the threshold sum value or threshold cost. Therefore, the equalizer 231 coupled to the optimizer 235 can dynamically provide a compensation function to compensate the signals Y₁-Y₄ for propagation effects and/or difference of unbalanced amplitudes, unbalanced phases, and/or unbalanced time-delays so as to improve the signals Z₁-Z₄. Since the dynamic optimization will assure the orthogonality among the four amplified outputs Z₁-Z₄, the low power diagnostic signal Z₄ is reconstituted and focused as the designated output port 7 d with leakage from other ports 7 a-7 c at least −35 dB below.

Alternatively, the system 300 can further include four frequency up-conversion components 316 a-316 d illustrated in FIG. 7D in four parallel signal paths or channels between four output ports 11 a-11 d of the equalizer 231 and four input ports 8 a-8 d of the power amplifiers 320 a-320 d. The system 300 illustrated in FIG. 7D is similar to that illustrated in FIG. 7C except that the system 300 illustrated in FIG. 7D further includes the frequency up-conversion components 316 a-316 d. In this case, the wave-front multiplexer 213 and equalizer 231 can process signals in baseband, for example. In FIG. 7D, the wave-front multiplexer 213 and the equalizer 231 can be, but not limited to, integrated or embedded in a module, processor, integrated-circuit chip, system-on chip or chip package 310, and the optimizer 235 can be, but not limited to, embedded in another module, processor, integrated-circuit chip, system-on chip or chip package. Alternatively, the wave-front multiplexer 213, the equalizer 231 and the optimizer 235 can be, but not limited to, integrated or embedded in the module, processor, integrated-circuit chip, system-on chip or chip package 310.

Referring to FIG. 7D, the process illustrated in FIG. 7D is similar to that illustrated in FIG. 7C except the following process. Referring to FIG. 7D, before the equalized signals W₁-W₄ are transmitted to the power amplifiers 320 a-320 d operating in near linear modes, the equalized signals W₁-W₄ can be alternatively sent in parallel to input ports 8 a-8 d of the frequency up-conversion components 316 a-316 d. Upon receiving the equalized signals W₁-W₄, the frequency up-conversion components 316 a-316 d can convert the signals W₁-W₄ into four analog or digital signals U₁-U₄ each having or modulating a distinct carrier within a distinct frequency sub-band in a bandwidth, such as Ku frequency band or Ka frequency band, for satellite communication, for example. The analog or digital signals U₁-U₄ can be output from output ports 9 a-9 d of the frequency up-conversion components 316 a-316 d respectively.

Referring to FIG. 7D, upon receiving the analog or digital signals U₁-U₄, the power amplifiers 320 a-320 d power the analog or digital signals U₁-U₄ by the same gain or different gains respectively and output four analog or digital signals S₁-S₄ in parallel from the four output ports 5 a-5 d of the power amplifiers 320 a-320 d. The operation and characteristics of the power amplifiers 320 a-320 d illustrated in FIG. 7D can be referred to as those illustrated in FIGS. 7A and 7B.

Alternatively, the system 300 can process the number N_(A) of input signals, wherein the input signals includes extraneous analog or digital signals from one or more extraneous systems, ground signals from a ground reference, and one or more pilot or diagnostic signals. The number of N_(A) could be any number equal to or greater than 2, 4, 8, 16, 32, 64, 128, 256 and so on. In this case illustrated in FIG. 7E, the system 300 processes eight input signals including four extraneous analog or digital signals X₁-X₄ input from one or more extraneous systems to ports 2 a, 2 e, 2 f and 2 g of the wave-front multiplexer 213, three ground signals from a ground reference to ports 2 b, 2 c and 2 d of the wave-front multiplexer 213, and a pilot or diagnostic signal X₅ input to a port 2 h of the wave-front multiplexer 213.

Referring to FIG. 7E, upon receiving the number N_(A) of input signals, such as eight input signals including the analog or digital signals X₁-X₄, the three ground signals and the pilot or diagnostic signal X₅, the wave-front multiplexer 213 processes the number N_(A) of the input signals into the number N_(A) of output signals, such as eight analog or digital signals Y₁-Y₈, by the above-mentioned wave-front multiplexing transform, which can be referred to as the description illustrated in FIGS. 1A and 1D. Each of the number N_(A) of the output signals is a linear combination, i.e. weighted sum, of the number N_(A) of the input signals multiplied by respective weightings, and distributions of the weightings of any two input components in all the number N_(A) of the output signals are orthogonal, which can be referred to as the description illustrated in FIGS. 1A and 1D. In this case, as illustrated in FIG. 1D, the number of H is equal to 8. The wave-front multiplexer 213 may include 8*8 computing units and eight summing processors. The computing units form a processor array with eight rows and eight columns. The extraneous signals X₁-X₄, the three ground signals and the pilot or diagnostic signal X₅ can be received by the computing units in the respective eight columns in the processor array. Upon receiving the input signals X₁-X₄, the three ground signals and the pilot or diagnostic signal X₅, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The eight summing processors can output the four signals Y₁-Y₈ each combined with the weighted signals output from the computing units in a corresponding one of the eight rows in the processor array. Each of the signals X₁-X₄ and pilot or diagnostic signal X₈ can be, but not limited to, an IF digital signal or a RF digital signal.

Next, referring to FIG. 7E, upon receiving the number N_(A) of the signals output from the wave-front multiplexer 213, such as the eight analog or digital signals Y₁-Y₈, the equalizer 231 performs an equalizing process to the number N_(A) of the signals, such as Y₁-Y₈, output from the wave-front multiplexer 213 such that the number N_(A) of the signals, such as Y₁-Y₈, output from the wave-front multiplexer 213 can be compensated to be multiplied by the number N_(A) of respective weightings, and then outputs the number N_(A) of equalized digital signals, such as the equalized digital signals W₁-W₈, respectively, from its the number N_(A) of output ports, such as the eight output ports 11 a-11 h. For example, the equalized digital signal W₁ is created by the equalizer 231 multiplying the analog or digital signal Y₁ by a weighting of the equalizer 231. The equalized digital signal W₂ is created by the equalizer 231 multiplying the analog or digital signal Y₂ by another weighting of the equalizer 231. The equalized digital signal W₃ is created by the equalizer 231 multiplying the analog or digital signal Y₃ by another weighting of the equalizer 231. The equalized digital signal W₄ is created by the equalizer 231 multiplying the analog or digital signal Y₄ by another weighting of the equalizer 231. The equalized digital signal W₅ is created by the equalizer 231 multiplying the analog or digital signal Y₅ by another weighting of the equalizer 231. The equalized digital signal W₆ is created by the equalizer 231 multiplying the analog or digital signal Y₆ by another weighting of the equalizer 231. The equalized digital signal W₇ is created by the equalizer 231 multiplying the analog or digital signal Y₇ by another weighting of the equalizer 231. The equalized digital signal W₈ is created by the equalizer 231 multiplying the analog or digital signal Y₈ by the other weighting of the equalizer 231. Each of the respective weightings of the equalizer 231 can be, but not limited to, a complex value such that the number N_(A) of equalized signals, such as the equalized signals W₁-W₈, can be rotated precisely to become in phase. In this case, the equalizer 231 can be performed by the narrow band equalizer, as illustrated in FIG. 1C. The narrow band equalizer 231 can provide phase and amplitude modifications to each of the number N_(A) of the signals output from the wave-front multiplexer 213, such as the signals Y₁-Y₈, featuring a constant phase shift and a constant amplitude attenuation across the narrow frequency band. Alternatively, the equalizer 231 can be performed by the broadband equalizer, as illustrated in FIG. 1C. The broadband equalizer 231 can provide phase and amplitude modifications to each of the number N_(A) of the signals output from the wave-front multiplexer 213, such as the signals Y₁-Y₈, featuring a constant phase shift and a constant amplitude attenuation in each sub-band across the broad frequency band, but the phase shift and amplitude attenuation in one sub-band across the broad frequency band is different from those in the other sub-band across the broad frequency band. In this case, the wave-front multiplexer 213 and equalizer 231 can process signals in baseband, for example.

Next, referring to FIG. 7E, the number N_(A) of the equalized signals, such as the eight equalized digital signals W₁-W₈, are transmitted in parallel to the number N_(A) of the input ports, such as eight input port 8 a-8 h, of the number N_(A) of the frequency up-conversion components, such as eight frequency up-conversion components 316 a-316 h. Upon receiving the number N_(A) of the equalized signals, such as W₁-W₈, the number N_(A) of the frequency up-conversion components, such as 316 a-316 h, can convert the number N_(A) of the signals, such as W₁-W₈, into the number N_(A) of up-converted signals, such as eight analog or digital signals U₁-U₈, each having or modulating a distinct carrier within a distinct frequency sub-band in a bandwidth, such as Ku frequency band or Ka frequency band, for satellite communication, for example. The number N_(A) of up-converted signals, such as U₁-U₈, can be output from the number N_(A) of output ports, such as eight output ports 9 a-9 h, of the number N_(A) of the frequency up-conversion components, such as 316 a-316 h, respectively.

Next, referring to FIG. 7E, the number N_(A) of the up-converted signals, such as the eight up-converted digital signals W₁-W₈, are transmitted in parallel to the number N_(A) of the input ports, such as the eight input port 4 a-4 h, of the number N_(A) of the power amplifiers, such as the eight power amplifiers 320 a-320 h, operating in near linear modes. Upon receiving the number N_(A) of the up-converted signals, such as U₁-U₈, the number N_(A) of the power amplifiers, such as 320 a-320 h, power the number N_(A) of the up-converted signals, such as U₁-U₈, by the same gain or different gains respectively and output the number N_(A) of powered signals, such as eight analog or digital signals S₁-S₈, in parallel from the number N_(A) of output ports, such as its eight output ports 5 a-5 h, of the number N_(A) of the power amplifiers, such as 320 a-320 h. For example, the analog or digital signal S₁ features the analog or digital signal W₁ powered by a first gain of the power amplifier 320 a. The analog or digital signal S₂ features the analog or digital signal W₂ powered by a second gain of the power amplifier 320 b. The analog or digital signal S₃ features the analog or digital signal W₃ powered by a third gain of the power amplifier 320 c. The analog or digital signal S₄ features the analog or digital signal W₄ powered by a fourth gain of the power amplifier 320 d. The analog or digital signal S₅ features the analog or digital signal W₅ powered by a fifth gain of the power amplifier 320 e. The analog or digital signal S₆ features the analog or digital signal W₆ powered by a sixth gain of the power amplifier 320 f The analog or digital signal S₇ features the analog or digital signal W₇ powered by a seventh gain of the power amplifier 320 g. The analog or digital signal S₈ features the analog or digital signal W₈ powered by an eighth gain of the power amplifier 320 h. In a case, the first through eighth gains can be substantially equal to one another. Alternatively, some of the first through eighth gains can be substantially equal to each other or one another, such as the first through fourth gains are substantially equal to one another, and the fifth through eighth gains are substantially equal to one another, and two of the first through eighth gains, such as first and fifth gains, can be different from each other. Alternatively, the first through eighth gains can be different from one another. The number N_(A) of the power amplifiers, such as 320 a-320 h, could be realized by the number N_(A) of integrated circuit chips embedded in a single chip package, by the number N_(A) of integrated circuit chips embedded in the number N_(A) of individual chip packages, or by a single integrated circuit chip. Alternatively, the function of the number N_(A) of the power amplifiers, such as 320 a-320 d, can be realized by software installed in the system 300.

Next, referring to FIG. 7E, upon receiving, in parallel, the number N_(A) of the powered signals, such as the eight powered signals S₁-S₈, the wave-front demultiplexer 232 extracts the number N_(A) of coherently combined signals, such as including five analog or digital signals Z₁-Z₅ and three ground signals, from the number N_(A) of the powered signals, such as S₁-S₈, by the above-mentioned wave-front demultiplexing transform. The number N_(A) of the extracted signals output from the wave-front demultiplexer 232 can be, in sequence, the number N_(A) of the input signals, input into the wave-front multiplexer 213, powered by substantially the same gain respectively or by different gains respectively. For example, the analog or digital signals Z₁-Z₅ can be the analog or digital signals X₁-X₅ powered by substantially the same gain respectively or by different gains respectively. The wave-front demultiplexing transform can be referred to as the description illustrated in FIGS. 1A and 1E. Each of the number N_(A) of the extracted signals, such as including five analog or digital signals Z₁-Z₅ and three ground signals, is a linear combination, i.e. weighted sum, of the number N_(A) of the powered signals, such as S₁-S₈, multiplied by respective weightings, and distributions of the weightings of any two input components in all the number N_(A) of the extracted signals, such as signals Z₁-Z₅ and three ground signals, are orthogonal, which can be referred to as the description illustrated in FIGS. 1A and 1E. In this case, the number of I is equal to 8. The wave-front demultiplexer 232 may include 8*8 computing units and eight summing processors. The computing units form a processor array with eight rows and eight columns. The input signals S₁-S₈ can be received by the computing units in the respective eight columns in the processor array. Upon receiving the input signals S₁-S₈, each of the computing units independently weights its received signal, multiplied by a weighting value, to generate a weighted signal. The eight summing processors can output the eight signals, including the analog or digital Z₁-Z₅ and the ground signals, each combined with the weighted signals output from the computing units in a corresponding one of the eight rows in the processor array. Each of the analog or digital signals Z₁-Z₅ can be, but not limited to, an IF digital signal or a RF digital signal.

Next, referring to FIG. 7E, an optimization process as illustrated in FIG. 7C can be performed. One of more of the number N_(A) of the input signals, input to the wave-front multiplexer 213, such as the signal X₅, can be input as a pilot or diagnostic signal. For example, the pilot or diagnostic signal X₅ may have a single frequency and fixed amplitude. Alternatively, the analog pilot or diagnostic signal X₅ could change based on time or could be any signal known by the system 300. The extraneous analog signals X₁-X₄ are unknown by the system 300 and input into the system 300 from an extraneous system. The optimizer 235 can be in a signal path between the wave-front demultiplexer 232 and the equalizer 231.

After the number N_(A) of the extracted signals are output from the wave-front demultiplexer 232, upon receiving the pilot or diagnostic signals, such as Z₅, the optimizer 235 shown in FIG. 7E is configured to calculate differences between values represented by the pilot or diagnostic signals, such as Z₅, and corresponding predetermined values known by the system 300, wherein the corresponding pilot or diagnostic signals, such as X₅, input into the wave-front multiplexer 213 at the same sequences as the corresponding pilot or diagnostic signals, such as Z₅, output from the wave-front demultiplexer 232, represent the predetermined values. Alternatively, upon receiving all of the number N_(A) of the extracted signals, such as the signals Z₁-Z₅ and the three ground signals, output from the wave-front demultiplexer 232, the optimizer 235 may be configured further to calculate a correlation between each two of the number N_(A) of the extracted signals. Next, the optimizer 235 is configured to calculate a sum value, i.e. cost, by performing weighted summation of multiple factors including the differences. Alternatively, the factors may further include the all correlations in case that the correlations are obtained. Next, the optimizer 235 is configured to compare the calculated sum value or cost with a threshold sum value, i.e. threshold cost. Next, the optimizer 235 is configured to calculate a variation in the calculated sum value or cost in response to finding the calculated sum value or cost is greater than the threshold sum value or threshold cost. The optimizer 235 creates one or more control signals CS (only one is shown) based on the variation and transmits the control signals CS to the equalizer 231 so as to adjust the number N_(A) of the weightings of the equalizer 231. The optimizer 235 is configured to stop the above loop in response to finding the calculated sum value or cost is less than the threshold sum value or threshold cost. Therefore, the equalizer 231 coupled to the optimizer 235 can dynamically provide a compensation function to compensate the number N_(A) of the signals, such as Y₁-Y₈, output from the wave-front multiplexer 213, for propagation effects and/or difference of unbalanced amplitudes, unbalanced phases, and/or unbalanced time-delays so as to improve the number N_(A) of the extracted signals, such as Z₁-Z₅.

Referring to FIG. 7E, the input ports 2 b-2 d of the wave-front multiplexer 213 and the output ports 7 b-7 d of the wave-front demultiplexer 232 are connected to a ground reference for a linearization processing. In FIG. 7E, the wave-front multiplexer 213 and the equalizer 231 can be, but not limited to, integrated or embedded in a module, processor, integrated-circuit chip, system-on chip or chip package 310, and the optimizer 235 can be, but not limited to, embedded in another module, processor, integrated-circuit chip, system-on chip or chip package. Alternatively, the wave-front multiplexer 213, the equalizer 231 and the optimizer 235 can be, but not limited to, integrated or embedded in the module, processor, integrated-circuit chip, system-on chip or chip package 310.

The above-mentioned embodiments of the present invention can be, but not limited to, applied to wireless communication system, fiber optical communication system, wire communication system, radio frequency communication system, satellite communication system, sonar communication system, radar communication system, laser communication system, internet communication system, communication system between a vehicle and a satellite, communication system between a least two vehicles, internal vehicle communication system between the various operating subsystems within a vehicle, or a communication system resulting from a combination of at least two of these communication systems therein.

The components, steps, features, benefits and advantages that have been discussed are merely illustrative. None of them, nor the discussions relating to them, are intended to limit the scope of protection in any way. Numerous other embodiments are also contemplated. These include embodiments that have fewer, additional, and/or different components, steps, features, benefits and advantages. These also include embodiments in which the components and/or steps are arranged and/or ordered differently.

In reading the present disclosure, one skilled in the art will appreciate that embodiments of the present disclosure can be implemented in hardware, software, firmware, or any combinations of such, and over one or more networks. Suitable software can include computer-readable or machine-readable instructions for performing methods and techniques (and portions thereof) of designing and/or controlling the implementation of the wave-front multiplexing and demultiplexing processes. Moreover, embodiments of the present disclosure can be, but not limited to, used in a wireless or physical communication between two systems, such as between two computers, between a computer and a mobile or smart phone, between two mobile or smart phones, between a computer and a storage device, between a mobile or smart phone and a storage device, between two storage devices, between a television and a ground station, between a television and a smart or mobile phone, between a television and a computer, between a television and a striage device, or between two ground stations.

Unless otherwise stated, all measurements, values, ratings, positions, magnitudes, sizes, and other specifications that are set forth in this specification, including in the claims that follow, are approximate, not exact. They are intended to have a reasonable range that is consistent with the functions to which they relate and with what is customary in the art to which they pertain. Furthermore, unless stated otherwise, the numerical ranges provided are intended to be inclusive of the stated lower and upper values. Moreover, unless stated otherwise, all material selections and numerical values are representative of preferred embodiments and other ranges and/or materials may be used.

The scope of protection is limited solely by the claims, and such scope is intended and should be interpreted to be as broad as is consistent with the ordinary meaning of the language that is used in the claims when interpreted in light of this specification and the prosecution history that follows, and to encompass all structural and functional equivalents thereof. 

What is claimed is:
 1. A broadband digital beam forming system comprising: a set of Q pre-processing modules, Q being an integer greater than or equal to 2, each of the Q preprocessing modules receiving a respective one of Q broadband input signal streams and outputting M narrowband signal streams, M being an integer greater than or equal to 2, the total number of narrowband signal streams outputted by the Q pre-processing modules being Q times M; and a set of M digital beam forming modules in communication with the Q preprocessing modules, each of the M digital beam forming modules receiving corresponding Q narrowband signal streams of the Q times M narrowband signal streams, and outputting R beam signals, R being an integer greater than or equal to 1, wherein each of the Q pre-processing modules comprises: a time-domain demultiplexer for transforming the respective one of the Q broadband input signal streams into L demultiplexed signals, L being an integer smaller than or equal to M; and a wavefront multiplexer coupled to the time-domain demultiplexer, the wavefront multiplexer receiving the L demultiplexed signals and M minus L diagnostic signals, performing linear combination operations on the L demultiplexed signals and the M minus L diagnostic signals, and outputting the M narrowband signal streams.
 2. The broadband digital beam forming system of claim 1 further comprising: a set of R post-processing modules in communication with the M digital beam forming modules, each of the R post-processing modules receiving M beam signals, each of the M beam signals being a corresponding one of the R beam signals from each of the M digital beam forming modules, and outputting a corresponding broadband output signal.
 3. The broadband digital beam forming system of claim 2, wherein each of the R post-processing modules comprises: an equalizer for receiving the M beam signals, applying weightings on the M beam signals, and generating M equalized signals; and a wavefront demultiplexer coupled to the equalizer, for receiving the M equalized signals, performing linear combination operations on the M equalized signals, and generating M wavefront demultiplexed signals; and a time-domain multiplexer module coupled to the wavefront demultiplexer, for receiving and performing time-domain multiplexing on L wavefront demultiplexed signals of the M wavefront demultiplexed signals, and generating the corresponding broadband output signal.
 4. The broadband digital beam forming system of claim 3, wherein L is smaller than M and wherein each of the R post-processing modules further comprises: an optimizer coupled to the wavefront demultiplexer and the equalizer, the optimizer receiving remaining M minus L wavefront demultiplexed signals of the M wavefront demultiplexed signals, generating a control signal based on the remaining M minus L wavefront demultiplexed signals, and outputting the control signal to the equalizer to adjust the weightings.
 5. The broadband digital beam forming system of claim 1, wherein Q is equal to 2^(n), n being an integer greater than or equal to 1, and wherein M is equal to 2^(k), k being an integer greater than or equal to
 1. 6. The broadband digital beam forming system of claim 1, wherein each of the M digital beam forming modules comprises: an array of Q times R computing units, each of the computing units receiving one of the corresponding Q narrowband signal streams and generating a weighted signal; and a summing module comprising R summing processors coupled to the array of Q times R computing units, each of the R summing processors receiving and summing corresponding ones of the weighted signals and generating a respective one of the R beam signals.
 7. A broadband digital beam forming system comprising: a set of Q pre-processing modules, Q being an integer greater than or equal to 2, each of the Q preprocessing modules receiving a respective one of Q broadband input signal streams and outputting M narrowband signal streams, M being an integer greater than or equal to 2, the total number of narrowband signal streams outputted by the Q pre-processing modules being Q times M; and a set of M digital beam forming modules in communication with the Q preprocessing modules, each of the M digital beam forming modules receiving corresponding Q narrowband signal streams of the Q times M narrowband signal streams, and outputting R beam signals, R being an integer greater than or equal to 1, wherein each of the Q pre-processing modules comprises: a time-domain demultiplexer for transforming the respective one of Q broadband input signal streams into L demultiplexed signals, L being an integer greater than M; a wavefront multiplexer coupled to the time-domain demultiplexer, the wavefront multiplexer receiving the L demultiplexed signals and J diagnostic signals, J being an integer greater than 0, performing linear combination operations on the L demultiplexed signals and the J diagnostic signals, and outputting L plus J wavefront multiplexed signals; and a time-domain multiplexer module coupled to the wavefront multiplexer for transforming the L plus J wavefront multiplexed signals into the M narrowband signal streams.
 8. The broadband digital beam forming system of claim 7 further comprising: a set of R post-processing modules in communication with the M digital beam forming modules, each of the R post-processing modules receiving M beam signals, each of the M beam signals being a corresponding one of the R beam signals from each of the M digital beam forming modules, and outputting a corresponding broadband output signal.
 9. The broadband digital beam forming system of claim 8, wherein each of the R post-processing modules comprises: a time-domain demultiplexer for receiving and transforming the M beam signals into L plus J demultiplexed signals; an equalizer coupled to the time-domain demultiplexer, for receiving the L plus J demultiplexed signals, applying weightings on the L plus J demultiplexed signals, and generating L plus J equalized signals; a wavefront demultiplexer coupled to the equalizer, for receiving the L plus J equalized signals, performing linear combination operations on the L plus J equalized signals and generating L plus J wavefront demultiplexed signals; and a time-domain multiplexer module coupled to the wavefront demultiplexer, for receiving and performing time-domain multiplexing on L wavefront demultiplexed signals of the L plus J wavefront demultiplexed signals, and generating the corresponding broadband output signal.
 10. The broadband digital beam forming system of claim 9, wherein each of the R post-processing modules further comprises: an optimizer coupled to the wavefront demultiplexer and the equalizer, the optimizer receiving remaining J wavefront demultiplexed signals of the L plus J wavefront demultiplexed signals, generating a control signal based on the remaining J wavefront demultiplexed signals, and outputting the control signal to the equalizer to adjust the weightings.
 11. A method for broadband digital beam forming, the method comprising the operations of: (a) providing a set of Q pre-processing modules, Q being an integer greater than or equal to 2; (b) receiving, by each of the Q preprocessing modules, a respective one of Q broadband input signal streams; (c) outputting, by each of the Q preprocessing modules, M narrowband signal streams, M being an integer greater than or equal to 2, the total number of narrowband signal streams outputted by the Q pre-processing modules being Q times M; (d) providing a set of M digital beam forming modules in communication with the Q preprocessing modules; (e) receiving, by each of the M digital beam forming modules, corresponding Q narrowband signal streams of the Q times M narrowband signal streams; and (f) outputting, by each of the M digital beam forming modules, R beam signals, R being an integer greater than or equal to 1, wherein the operation (a) comprises: providing, for each of the Q pre-processing modules, a time-domain demultiplexer and a wavefront multiplexer coupled to the time-domain demultiplexer; and wherein the operations (b) and (c) comprise: transforming, by the time-domain demultiplexer, the respective one of the Q broadband input signal streams into L demultiplexed signals, L being an integer smaller than or equal to M; receiving, by the wavefront multiplexer, the L demultiplexed signals and M minus L diagnostic signals; performing, by the wavefront multiplexer, linear combination operations on the L demultiplexed signals and the M minus L diagnostic signals; and outputting, by the wavefront multiplexer, the M narrowband signal streams.
 12. The method of claim 11 further comprising the operations of: (g) providing a set of R post-processing modules in communication with the M digital beam forming modules; (h) receiving by each of the R post-processing modules M beam signals, each of the M beam signals being a corresponding one of the R beam signals from each of the M digital beam forming modules; and (i) outputting by each of the R post-processing modules a corresponding broadband output signal.
 13. The method of claim 12, wherein the operation (g) comprises: providing, for each of the R post-processing modules, an equalizer, a wavefront demultiplexer coupled to the equalizer, and a time-domain multiplexer module coupled to the wavefront demultiplexer; and wherein the operations (h) and (i) comprise: receiving, by the equalizer, the M beam signals; applying, by the equalizer, weightings on the M beam signals; generating, by the equalizer, M equalized signals; receiving, by the wavefront demultiplexer, the M equalized signals; performing, by the wavefront demultiplexer, linear combination operations on the M equalized signals; generating, by the wavefront demultiplexer, M wavefront demultiplexed signals; receiving, by the time-domain multiplexer module, L wavefront demultiplexed signals of the M wavefront demultiplexed signals; performing, by the time-domain multiplexer module, time-domain multiplexing on the L wavefront demultiplexed signals; and generating, by the time-domain multiplexer module, the corresponding broadband output signal.
 14. The method of claim 13, wherein L is smaller than M, wherein the operation (g) further comprises: providing, for each of the R post-processing modules, an optimizer coupled to the wavefront demultiplexer and the equalizer; and wherein the operations (h) and (i) further comprise: receiving, by the optimizer, remaining M minus L wavefront demultiplexed signals of the M wavefront demultiplexed signals; generating, by the optimizer, a control signal based on the remaining M minus L wavefront demultiplexed signals; and outputting, by the optimizer, the control signal to the equalizer to adjust the weightings.
 15. The method of claim 11, wherein Q is equal to 2^(n), n being an integer greater than or equal to 1, and wherein M is equal to 2^(k), k being an integer greater than or equal to
 1. 16. The method of claim 11, wherein the operation (d) comprises: providing, for each of the M digital beam forming modules, an array of Q times R computing units and a summing module comprising R summing processors coupled to the array of Q times R computing units; and wherein the operations (e) and (f) comprise: receiving, by each of the computing units, one of the corresponding Q narrowband signal streams; generating, by each of the computing units, a weighted signal; receiving, by each of the R summing processors, corresponding ones of the weighted signals; summing, by each of the R summing processors, the corresponding ones of the weighted signals; and generating, by each of the R summing processors, a respective one of the R beam signals.
 17. A method for broadband digital beam forming, comprising the operations of: (a) providing a set of Q pre-processing modules, Q being an integer greater than or equal to 2; (b) receiving, by each of the Q preprocessing modules, a respective one of Q broadband input signal streams; (c) outputting, by each of the Q preprocessing modules, M narrowband signal streams, M being an integer greater than or equal to 2, the total number of narrowband signal streams outputted by the Q pre-processing modules being Q times M; (d) providing a set of M digital beam forming modules in communication with the Q preprocessing modules; (e) receiving, by each of the M digital beam forming modules, corresponding Q narrowband signal streams of the Q times M narrowband signal streams; and (f) outputting, by each of the M digital beam forming modules, R beam signals, R being an integer greater than or equal to 1, wherein the operation (a) comprises: providing, for each of the Q pre-processing modules, a time-domain demultiplexer, a wavefront multiplexer coupled to the time-domain demultiplexer, and a time-domain multiplexer module coupled to the wavefront multiplexer; and wherein the operations (b) and (c) comprise: transforming, by the time-domain demultiplexer, the respective one of Q broadband input signal streams into L demultiplexed signals, L being an integer greater than M; receiving, by the wavefront multiplexer, the L demultiplexed signals and J diagnostic signals, J being an integer greater than 0; performing, by the wavefront multiplexer, linear combination operations on the L demultiplexed signals and the J diagnostic signals; outputting, by the wavefront multiplexer, L plus J wavefront multiplexed signals; and transforming, by the time-domain multiplexer module, the L plus J wavefront multiplexed signals into the M narrowband signal streams.
 18. The method of claim 17 further comprising the operations of: (g) providing a set of R post-processing modules in communication with the M digital beam forming modules; (h) receiving by each of the R post-processing modules M beam signals, each of the M beam signals being a corresponding one of the R beam signals from each of the M digital beam forming modules; and (i) outputting by each of the R post-processing modules a corresponding broadband output signal.
 19. The method of claim 18, wherein the operation (g) comprises: providing, for each of the R post-processing modules, a time-domain demultiplexer, an equalizer coupled to the time-domain demultiplexer, a wavefront demultiplexer coupled to the equalizer, and a time-domain multiplexer module coupled to the wavefront demultiplexer; and wherein the operations (h) and (i) comprise: receiving, by the time-domain demultiplexer, for receiving the M beam signals; transforming, by the time-domain demultiplexer, the M beam signals into L plus J demultiplexed signals; receiving, by the equalizer, the L plus J demultiplexed signals; applying, by the equalizer, weightings on the L plus J demultiplexed signals; generating, by the equalizer, L plus J equalized signals; receiving, by the wavefront demultiplexer, the L plus J equalized signals; performing, by the wavefront demultiplexer, linear combination operations on the L plus J equalized signals; generating, by the wavefront demultiplexer, L plus J wavefront demultiplexed signals; receiving, by the time-domain multiplexer module, [M]L wavefront demultiplexed signals of the L plus J wavefront demultiplexed signals; performing, by the time-domain multiplexer module, time-domain multiplexing on the L wavefront demultiplexed signals; and generating, by the time-domain multiplexer module, the corresponding broadband output signal.
 20. The method of claim 19, wherein the operation (g) further comprises: providing, for each of the R post-processing modules, an optimizer coupled to the wavefront demultiplexer and the equalizer; and wherein the operations (h) and (i) further comprise: receiving, by the optimizer, remaining J wavefront demultiplexed signals of the L plus J wavefront demultiplexed signals; generating, by the optimizer, a control signal based on the remaining J wavefront demultiplexed signals; and outputting, by the optimizer, the control signal to the equalizer to adjust the weightings. 